A hole is an opening in or through a particular medium, usually a solid body. Holes occur through natural and artificial processes, and may be useful for various purposes, or may represent a problem needing to be addressed in many fields of engineering. Depending on the material and the placement, a hole may be an indentation in a

surface A surface, as the term is most generally used, is the outermost or uppermost layer of a physical object or space. It is the portion or region of the object that can first be perceived by an observer using the senses of sight and touch, and is ...

(such as a hole in the ground), or may pass completely through that surface (such as a hole created by a hole puncher in a piece of paper).

Types

Holes can occur for a number of reasons, including natural processes and intentional actions by humans or animals. Holes in the ground that are made intentionally, such as holes made while searching for food, for replanting trees, or

posthole In archaeology a posthole or post-hole is a cut feature used to hold a surface timber or stone. They are usually much deeper than they are wide; however, truncation may not make this apparent. Although the remains of the timber may survive, most ...

s made for securing an object, are usually made through the process of

digging Digging, also referred to as excavation, is the process of using some implement such as claws, hands, manual tools or heavy equipment, to remove material from a solid surface, usually soil, sand or rock on the surface of Earth. Digging is act ...

. Unintentional holes in an object are often a sign of

damage Damage is any change in a thing, often a physical object, that degrades it away from its initial state. It can broadly be defined as "changes introduced into a system that adversely affect its current or future performance".Farrar, C.R., Sohn, H., ...

Pothole A pothole is a depression in a road surface, usually asphalt pavement, where traffic has removed broken pieces of the pavement. It is usually the result of water in the underlying soil structure and traffic passing over the affected area. Wate ...

s and

sinkhole A sinkhole is a depression or hole in the ground caused by some form of collapse of the surface layer. The term is sometimes used to refer to doline, enclosed depressions that are locally also known as ''vrtače'' and shakeholes, and to openi ...

s can damage human settlements. Holes can occur in a wide variety of materials, and at a wide range of scales. The smallest holes observable by humans include pinholes and

perforation A perforation is a small hole in a thin material or web. There is usually more than one perforation in an organized fashion, where all of the holes collectively are called a ''perforation''. The process of creating perforations is called perfor ...

s, but the smallest phenomenon described as a hole is an

electron hole In physics, chemistry, and electronic engineering, an electron hole (often simply called a hole) is a quasiparticle which is the lack of an electron at a position where one could exist in an atom or atomic lattice. Since in a normal atom or ...

, which is a position in an

atom Every atom is composed of a nucleus and one or more electrons bound to the nucleus. The nucleus is made of one or more protons and a number of neutrons. Only the most common variety of hydrogen has no neutrons. Every solid, liquid, gas, a ...

or atomic lattice where an

electron The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have n ...

is missing. The largest phenomenon described as a hole is a

supermassive black hole A supermassive black hole (SMBH or sometimes SBH) is the largest type of black hole, with its mass being on the order of hundreds of thousands, or millions to billions of times the mass of the Sun (). Black holes are a class of astronomical ob ...

, an astronomical object which can be billions of times more massive than Earth's

sun The Sun is the star at the center of the Solar System. It is a nearly perfect ball of hot plasma, heated to incandescence by nuclear fusion reactions in its core. The Sun radiates this energy mainly as light, ultraviolet, and infrared radi ...

. The deepest hole on Earth is the man-made

Kola Superdeep Borehole The Kola Superdeep Borehole (russian: Кольская сверхглубокая скважина, translit=Kol'skaya sverkhglubokaya skvazhina) SG-3 is the result of a scientific drilling project of the Soviet Union in the Pechengsky District ...

, with a true vertical drill-depth of more than 7.5 miles (12 kilometers), which is only a fraction of the nearly 4,000 mile (6,400 kilometer) distance to the center of the Earth.

In mathematics

mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

, holes are examined in a number of ways. One of these is in homology, which is a general way of associating certain algebraic objects to other mathematical objects such as

topological space In mathematics, a topological space is, roughly speaking, a geometrical space in which closeness is defined but cannot necessarily be measured by a numeric distance. More specifically, a topological space is a set whose elements are called poin ...

s. Homology groups were originally defined in

algebraic topology Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariants that classify topological spaces up to homeomorphism, though usually most classify ...

, and homology was originally a rigorous mathematical method for defining and categorizing holes in a mathematical object called a

manifold In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point. More precisely, an n-dimensional manifold, or ''n-manifold'' for short, is a topological space with the property that each point has a n ...

. The initial motivation for defining homology groups was the observation that two shapes can be distinguished by examining their holes. For instance, a circle is not a disk because the circle has a hole through it while the disk is solid, and the ordinary sphere is not a circle because the sphere encloses a two-dimensional hole while the circle encloses a one-dimensional hole. Because a hole is immaterial, it is not immediately obvious how to define one or distinguish it from others. Another is the notion of

homotopy group In mathematics, homotopy groups are used in algebraic topology to classify topological spaces. The first and simplest homotopy group is the fundamental group, denoted \pi_1(X), which records information about loops in a space. Intuitively, homotop ...

: these are invariants of a topological space that, when non-trivial (one also says in this case that the space is not

k-connected In algebraic topology, homotopical connectivity is a property describing a topological space based on the dimension of its holes. In general, low homotopical connectivity indicates that the space has at least one low-dimensional hole. The concep ...

), detect the presence of "holes" in the sense that the space contains a

sphere A sphere () is a geometrical object that is a three-dimensional analogue to a two-dimensional circle. A sphere is the set of points that are all at the same distance from a given point in three-dimensional space.. That given point is the c ...

that cannot be contracted to a point. The term of hole is often used informally when discussing these objects. For surfaces a notion closer to the intuitive meaning exists: the

genus Genus ( plural genera ) is a taxonomic rank used in the biological classification of living and fossil organisms as well as viruses. In the hierarchy of biological classification, genus comes above species and below family. In binomial nom ...

of a connected,

orientable In mathematics, orientability is a property of some topological spaces such as real vector spaces, Euclidean spaces, surfaces, and more generally manifolds that allows a consistent definition of "clockwise" and "counterclockwise". A space i ...

is an

integer An integer is the number zero (), a positive natural number (, , , etc.) or a negative integer with a minus sign ( −1, −2, −3, etc.). The negative numbers are the additive inverses of the corresponding positive numbers. In the languag ...

representing the maximum number of cuttings along non-intersecting closed simple

curve In mathematics, a curve (also called a curved line in older texts) is an object similar to a line, but that does not have to be straight. Intuitively, a curve may be thought of as the trace left by a moving point. This is the definition that ...

s without rendering the resultant

disconnected. In layman's terms, it is exactly the number of "holes" the surface has, when represented as a submanifold in 3-space.

In physics

In physics,

antimatter In modern physics, antimatter is defined as matter composed of the antiparticles (or "partners") of the corresponding particles in "ordinary" matter. Antimatter occurs in natural processes like cosmic ray collisions and some types of radioac ...

is pervasively described as a hole, a location that, when brought together with ordinary matter to fill the hole, results in both the hole and the matter cancelling each-other out. This is analogous to patching a pothole with asphalt, or filling a bubble below the surface of water with an equal amount of water to cancel it out. The most direct example is the

; a fairly general theoretical description is provided by the

Dirac sea The Dirac sea is a theoretical model of the vacuum as an infinite sea of particles with negative energy. It was first postulated by the British physicist Paul Dirac in 1930 to explain the anomalous negative-energy quantum states predicted by th ...

, which treats

positron The positron or antielectron is the antiparticle or the antimatter counterpart of the electron. It has an electric charge of +1 '' e'', a spin of 1/2 (the same as the electron), and the same mass as an electron. When a positron collide ...

s (or anti-particles in general) as holes. Holes provide one of the two primary forms of conduction in a

semi-conductor A semiconductor is a material which has an electrical conductivity value falling between that of a conductor, such as copper, and an insulator, such as glass. Its resistivity falls as its temperature rises; metals behave in the opposite way. ...

, that is, the material from which

transistor upright=1.4, gate (G), body (B), source (S) and drain (D) terminals. The gate is separated from the body by an insulating layer (pink). A transistor is a semiconductor device used to Electronic amplifier, amplify or electronic switch, switch ...

s are made; without holes, current could not flow, and transistors turn on and off by enabling or disabling the creation of holes.

In biology

Animal bodies tend to contain specialized holes which serve various biological functions, such as the intake of oxygen or food, the excretion of waste, and the intake or expulsion of other fluids for reproductive purposes. In some simple animals, a single hole serves all of these purposes. The formation of holes is a significant event in the development of an animal:

Gramicidin A Gramicidin, also called gramicidin D, is a mix of ionophoric antibiotics, gramicidin A, B and C, which make up about 80%, 5%, and 15% of the mix, respectively. Each has 2 isoforms, so the mix has 6 different types of gramicidin molecules. They c ...

, a

polypeptide Peptides (, ) are short chains of amino acids linked by peptide bonds. Long chains of amino acids are called proteins. Chains of fewer than twenty amino acids are called oligopeptides, and include dipeptides, tripeptides, and tetrapeptides. ...

with a helical shape, has been described as a portable hole. When it forms a

dimer Dimer may refer to: * Dimer (chemistry), a chemical structure formed from two similar sub-units ** Protein dimer, a protein quaternary structure ** d-dimer * Dimer model, an item in statistical mechanics, based on ''domino tiling'' * Julius Dimer ( ...

, it can embed itself in cellular bilayer membranes and form a hole through which water molecules can pass.

Blind and through

engineering Engineering is the use of scientific principles to design and build machines, structures, and other items, including bridges, tunnels, roads, vehicles, and buildings. The discipline of engineering encompasses a broad range of more speciali ...

machining Machining is a process in which a material (often metal) is cut to a desired final shape and size by a controlled material-removal process. The processes that have this common theme are collectively called subtractive manufacturing, which utilizes ...

, and

tooling Tooling may refer to: * Machine tools and the tooling, such as cutting tools, fixtures, and accessories, that is used on them ** Cutting tool (machining), any of hundreds of kinds of cutters ** Fixture (tool), a fixed workholding or support device ...

, a hole may be a blind hole or a through hole (also called a thru-hole or clearance hole). A blind hole is a hole that is

ream Ream may refer to: * Paper ream, unit of 500 sheets of paper * Ream (surname) * Reamer, tool used to widen a hole * Ream, West Virginia * Ream, the name of Rama in the Khmer version of the Ramayana, the Reamker ''Reamker'' ( km, រាមក� ...

ed,

drill A drill is a tool used for making round holes or driving fasteners. It is fitted with a bit, either a drill or driver chuck. Hand-operated types are dramatically decreasing in popularity and cordless battery-powered ones proliferating due to ...

ed, or milled to a specified depth without breaking through to the other side of the workpiece. A through hole is a hole that is made to go completely through the material of an object. In other words, a through hole is a hole that goes all the way through something. Taps used for through holes are generally tapered since it will tap faster and the chips will be released when the tap exits the hole. The etymology of the ''blind'' hole is that it is not possible to see through it. It may also refer to any feature that is taken to a specific depth, more specifically referring to internally threaded hole (tapped holes). Not considering the drill point, the depth of the blind hole, conventionally, may be slightly deeper than that of the threaded depth. There are three accepted methods of threading blind holes: # Conventional

tapping Tapping is a playing technique that can be used on any stringed instrument, but which is most commonly used on guitar. The technique involves a string being fretted and set into vibration as part of a single motion. This is in contrast to stand ...

, especially with bottom taps # Single-point threading, where the workpiece is rotated, and a pointed cutting tool is fed into the workpiece at the same rate as the pitch of the internal thread. Single-pointing inside a blind hole, like boring inside one, is inherently more challenging than doing so in a through hole. This was especially true in the era when manual machining was the only method of control. Today, CNC makes these tasks less stressful, but nevertheless still more challenging than with through holes. # Helical interpolation, where the workpiece remains stationary and

Computer Numerical Control Numerical control (also computer numerical control, and commonly called CNC) is the automated control of machining tools (such as drills, lathes, mills, grinders, routers and 3D printers) by means of a computer. A CNC machine processes a p ...

(CNC) moves a

milling cutter Milling cutters are cutting tools typically used in milling machines or machining centres to perform milling operations (and occasionally in other machine tools). They remove material by their movement within the machine (e.g., a ball nose mill ...

in the correct helical path for a given thread, milling the thread. At least two U.S. tool manufacturers have manufactured tools for

thread milling In manufacturing, threading is the process of creating a screw thread. More screw threads are produced each year than any other machine element. There are many methods of generating threads, including subtractive methods (many kinds of thread cu ...

in blind holes: Ingersoll Cutting Tools of Rockford, Illinois, and Tooling Systems of Houston, Texas, who introduced the Thread Mill in 1977, a device that milled large internal threads in the blind holes of oil well

blowout preventer A blowout preventer (BOP) (pronounced B-O-P, not "bop") is a specialized valve or similar mechanical device, used to seal, control and monitor oil and gas wells to prevent blowouts, the uncontrolled release of crude oil or natural gas from a w ...

s. Today many CNC milling machines can run such a thread milling cycle (see a video of such a cut in the "External links" section). One use of through holes in electronics is with

through-hole technology In electronics, through-hole technology (also spelled "thru-hole") is a manufacturing scheme in which leads on the components are inserted through holes drilled in printed circuit boards (PCB) and soldered to pads on the opposite side, eithe ...

, a mounting scheme involving the use of

lead Lead is a chemical element with the symbol Pb (from the Latin ) and atomic number 82. It is a heavy metal that is denser than most common materials. Lead is soft and malleable, and also has a relatively low melting point. When freshly cut, ...

s on the components that are inserted into holes drilled in

printed circuit board A printed circuit board (PCB; also printed wiring board or PWB) is a medium used in electrical and electronic engineering to connect electronic components to one another in a controlled manner. It takes the form of a laminated sandwich str ...

s (PCB) and

soldered Solder (; NA: ) is a fusible metal alloy used to create a permanent bond between metal workpieces. Solder is melted in order to wet the parts of the joint, where it adheres to and connects the pieces after cooling. Metals or alloys suitable ...

to pads on the opposite side either by manual assembly (hand placement) or by the use of automated insertion mount machines.

Pinholes

A pinhole is a small hole, usually made by pressing a thin, pointed object such as a pin through an easily penetrated material such as a

fabric Textile is an umbrella term that includes various fiber-based materials, including fibers, yarns, filaments, threads, different fabric types, etc. At first, the word "textiles" only referred to woven fabrics. However, weaving is not ...

or a very thin layer of

metal A metal (from ancient Greek, Greek μέταλλον ''métallon'', "mine, quarry, metal") is a material that, when freshly prepared, polished, or fractured, shows a lustrous appearance, and conducts electrical resistivity and conductivity, e ...

. Similar holes made by other means are also often called pinholes. Pinholes may be intentionally made for various reasons. For example, in

optics Optics is the branch of physics that studies the behaviour and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behaviour of visible, ultrav ...

pinhole A hole is an opening in or through a particular medium, usually a solid body. Holes occur through natural and artificial processes, and may be useful for various purposes, or may represent a problem needing to be addressed in many fields of en ...

s are used as

aperture In optics, an aperture is a hole or an opening through which light travels. More specifically, the aperture and focal length of an optical system determine the cone angle of a bundle of rays that come to a focus in the image plane. An ...

s to select certain rays of light. This is used in

pinhole camera A pinhole camera is a simple camera without a lens but with a tiny aperture (the so-called '' pinhole'')—effectively a light-proof box with a small hole in one side. Light from a scene passes through the aperture and projects an inverted image ...

s to form an image without the use of a

lens A lens is a transmissive optical device which focuses or disperses a light beam by means of refraction. A simple lens consists of a single piece of transparent material, while a compound lens consists of several simple lenses (''elements ...

. Pinholes on

produce Produce is a generalized term for many farm-produced crops, including fruits and vegetables ( grains, oats, etc. are also sometimes considered ''produce''). More specifically, the term ''produce'' often implies that the products are fres ...

packaging have been used to control the atmosphere and relative humidity within the packaging. In many fields, pinholes are a harmful side effect of manufacturing processes. For example, in the assembly of

microcircuit An integrated circuit or monolithic integrated circuit (also referred to as an IC, a chip, or a microchip) is a set of electronic circuits on one small flat piece (or "chip") of semiconductor material, usually silicon. Large numbers of tiny M ...

s, pinholes in the

dielectric In electromagnetism, a dielectric (or dielectric medium) is an electrical insulator that can be polarised by an applied electric field. When a dielectric material is placed in an electric field, electric charges do not flow through the ma ...

insulator layer coating the circuit can cause the circuit to fail. Therefore, " avoid pinholes that might protrude through the entire thickness of the dielectric layer, it is a common practice to screen several layers of dielectric with drying and firing after each screening", thereby preventing the pinholes from becoming continuous.

Philosophy and psychology

It has been noted that holes occupy an unusual ontological position in philosophy, as people tend to refer to them as tangible and countable objects, when in fact they are the absence of something in another object. In the study of visual perception, a hole is a special case of figure-ground, because the ground region is entirely surrounded by the figure. For a region to be perceived as a visual hole three factors are important: depth factors indicating that the enclosed region lies behind; grouping between the enclosed region and the surround; and figural factors (for example symmetry, convexity, or familiarity) that lead to the perception of a figure rather than a hole. There is a debate on whether holes are special and whether they are perceived as having their own shape. They may be special in some cases, but not in the ownership of the contours. Some people have an aversion to the sight of irregular patterns or clusters of small holes, a condition called

trypophobia Trypophobia is an aversion to the sight of irregular patterns or clusters of small holes or bumps. It is not officially recognized as a mental disorder, but may be diagnosed as a specific phobia if excessive fear and distress occur. Most affec ...

. Researchers hypothesize that this is the result of a biological revulsion that associates trypophobic shapes with danger or disease, and may therefore have an

evolutionary Evolution is change in the heritable characteristics of biological populations over successive generations. These characteristics are the expressions of genes, which are passed on from parent to offspring during reproduction. Variati ...

basis.

In Culture and as a Metaphor

An example of the use of holes in popular culture can be found in the

Beatles The Beatles were an English rock band, formed in Liverpool in 1960, that comprised John Lennon, Paul McCartney, George Harrison and Ringo Starr. They are regarded as the most influential band of all time and were integral to the developm ...

lyric from the song, " A Day in the Life", from their 1967 album ''

Sgt. Pepper's Lonely Hearts Club Band ''Sgt. Pepper's Lonely Hearts Club Band'' is the eighth studio album by the English rock band the Beatles. Released on 26May 1967, ''Sgt. Pepper'' is regarded by musicologists as an early concept album that advanced the roles of sound composi ...

'': The reference to 4,000 holes was written by

John Lennon John Winston Ono Lennon (born John Winston Lennon; 9 October 19408 December 1980) was an English singer, songwriter, musician and peace activist who achieved worldwide fame as founder, co-songwriter, co-lead vocalist and rhythm guitarist of ...

, and inspired by a ''Far & Near'' news brief from the same 17 January edition of the ''Daily Mail'', which had also provided inspiration for previous verses of the song. Under the headline "The holes in our roads", the brief stated: "There are 4,000 holes in the road in Blackburn, Lancashire, or one twenty-sixth of a hole per person, according to a council survey. If Blackburn is typical, there are two million holes in Britain's roads and 300,000 in London". Holes have also been described as ontological parasites because they can only exist as aspects of another object. The psychological concept of a hole as a physical object is taken to its logical extreme in the fictional concept of a

portable hole In various works of fiction, a portable hole is a two-dimensional device that can be used to contravene the laws of physics by creating a passage through a solid surface, through which characters can move. Notable uses The 1955 '' Looney Tunes'' ...

, exemplified in

role-playing game A role-playing game (sometimes spelled roleplaying game, RPG) is a game in which players assume the roles of characters in a fictional setting. Players take responsibility for acting out these roles within a narrative, either through literal ac ...

s and characterized as a "hole" that a person can carry with them, keep things in, and enter themselves as needed. In art holes are sometimes referred to as

negative space Negative space, in art, is the empty space around and between the subject(s) of an image. Negative space may be most evident when the space around a subject, not the subject itself, forms an interesting or artistically relevant shape, and s ...

, as in the case of the Japanese concept of Ma. Holes can also be referenced metaphorically as existing in non-tangible things. For example, a person who provides an account of an event that lacks important details can be said to have "holes in their story", and a fictional work with unexplained narrative elements can be said to have

plot hole In fiction, a plot hole, plothole or plot error is a gap or inconsistency in a storyline that goes against the flow of logic established by the story's plot. Plot holes are usually created unintentionally, often as a result of editing or the w ...

s. A person who has suffered loss is often referred to as having a "hole in their heart". The concept of a "God-shaped hole" occurs in religious discourse:

Unicode

The

Unicode Unicode, formally The Unicode Standard,The formal version reference is is an information technology standard for the consistent encoding, representation, and handling of text expressed in most of the world's writing systems. The standard, ...

symbol for HOLE, U+1F573, was approved in 2014 as part of the Miscellaneous Symbols and Pictographs chart in Unicode 7.0, and was part of Emoji 1.0, published in 2015. As pictorial representations for emoji are platform-dependent, Emojipedia shows images of the hole symbol as depicted on various platforms.

Gallery

LiščíNoraVsž1.JPG, Hole in the ground dug by a fox as its burrow. Bangalay-bird-hollow.jpg, Hole in a Eucalyptus tree used as a nest by Lorikeets. Two Arecaceae in the fields viewed through a hole in a tree trunk in Laos at sunrise.jpg, Trees visible through a large hole in a tree trunk in Laos. Trees and clouds with a hole, Karawanks, Slovenia.jpg, Hole in a cloud over Karawanks, Slovenia. 靴下にデカい穴があいてた.jpg, Sock with a hole in it. BH LMC.png, Simulated view of a black hole in front of the Large Magellanic Cloud. Black hole - Messier 87 crop max res.jpg, First image of a black hole by the Event Horizon Telescope. Plated-through_holes_on_an_electronic_circuit_board.jpg, Close-up view of an electronic circuit board showing component lead holes (gold-plated) with through-hole plating. Ovation guitar sound holes horizontal.jpg,

Sound hole A sound hole is an opening in the body of a stringed musical instrument, usually the upper sound board. Sound holes have different shapes: * round in flat-top guitars and traditional bowl-back mandolins; * F-holes in instruments from the vio ...

s precisely carved into the surface of a

guitar The guitar is a fretted musical instrument that typically has six strings. It is usually held flat against the player's body and played by strumming or plucking the strings with the dominant hand, while simultaneously pressing selected string ...

can facilitate a desired sound. Well, if you know of a better 'ole, go to it.jpg,

First World War World War I (28 July 1914 11 November 1918), often abbreviated as WWI, was List of wars and anthropogenic disasters by death toll, one of the deadliest global conflicts in history. Belligerents included much of Europe, the Russian Empire, ...

cartoon ''Well, if you knows of a better 'ole, go to it'' by

Bruce Bairnsfather Captain Charles Bruce Bairnsfather (9 July 188729 September 1959) was a prominent British humorist and cartoonist. His best-known cartoon character is Old Bill. Bill and his pals Bert and Alf featured in Bairnsfather's weekly "Fragments from Fr ...

, 1915. Hole in berlin wall.jpg, A hole in the

Berlin wall The Berlin Wall (german: Berliner Mauer, ) was a guarded concrete barrier that encircled West Berlin from 1961 to 1989, separating it from East Berlin and East Germany (GDR). Construction of the Berlin Wall was commenced by the gover ...

, 2019. Single-hole-punch.jpg, A handheld hole punch, used to make holes in paper and similar materials.

References

{{reflist, refs= {{Cite news , url=https://www.economist.com/news/science-and-technology/21700370-researchers-are-inventing-new-ways-prevent-motoring-curse-hole-story , title=The hole story , newspaper=

The Economist ''The Economist'' is a British weekly newspaper printed in demitab format and published digitally. It focuses on current affairs, international business, politics, technology, and culture. Based in London, the newspaper is owned by The Eco ...

, access-date=2017-02-11 , date=2016-06-11 {{Cite web , url=http://www.iflscience.com/environment/deepest-hole-world/ , title=What's At The Bottom Of The Deepest Hole On Earth? , access-date=2016-08-17 Richeson, D.; '' Euler's Gem: The Polyhedron Formula and the Birth of Topology'', Princeton University (2008), p. 254. {{cite book , title=Intuitive Concepts in Elementary Topology , series=Dover Books on Mathematics , author-first=Bradford Henry , author-last=Arnold , publisher=Courier /

Dover Publications Dover Publications, also known as Dover Books, is an American book publisher founded in 1941 by Hayward and Blanche Cirker. It primarily reissues books that are out of print from their original publishers. These are often, but not always, books ...

, date=2013 , isbn=978-0-48627576-5 , page=58 , url=https://books.google.com/books?id=TsbDAgAAQBAJ&pg=PA58 {{Cite Matousek 2007, Section 4.3 Munkres, James R. Topology. Vol. 2. Upper Saddle River: Prentice Hall, 2000. {{cite web , url=https://www.nature.com/scitable/blog/creature-cast/a_tale_of_two_holes , title=A tale of two holes – Creature Cast – Learn Science at Scitable , website=www.nature.com , author-first=Casey , author-last=Dunn , date=2009-11-06 {{Cite book , last=Mouritsen , first=Ole G. , url=https://www.worldcat.org/title/life-as-a-matter-of-fat-the-emerging-science-of-lipidomics/oclc/1156049123 , title=Life - As a Matter of Fat: The Emerging Science of Lipidomics , publisher=Springer , date=2005 , isbn=978-3-54023248-3 , pages=186 , oclc=1156049123 ''Electronic Packaging: Solder Mounting Technologies'' in K. H. Buschow et al (eds.), ''Encyclopedia of Materials: Science and Technology'',

Elsevier Elsevier () is a Dutch academic publishing company specializing in scientific, technical, and medical content. Its products include journals such as '' The Lancet'', '' Cell'', the ScienceDirect collection of electronic journals, '' Trends'', ...

, 2001 {{ISBN, 0-08-043152-6, pp. 2708–2709 {{cite book , title=The art of electronics , date=1989 , publisher=

Cambridge University Press Cambridge University Press is the university press of the University of Cambridge. Granted letters patent by King Henry VIII in 1534, it is the oldest university press in the world. It is also the King's Printer. Cambridge University Pr ...

, location=Cambridge , isbn=978-0-52137095-0 , edition=2nd , author-last1=Horowitz , author-first1=Paul , author-last2=Hill , author-first2=Winfield , url-access=registration , url=https://archive.org/details/artofelectronics00horo What is a Pinhole Camera?
''pinhole.cz''. Enrique Ortega-Rivas, ''Processing Effects on Safety and Quality of Foods'' (2010), p. 280. James J. Licari, Leonard R. Enlow, ''Hybrid Microcircuit Technology Handbook, 2nd Edition'' (2008), p. 162. {{cite book , url=https://plato.stanford.edu/archives/spr2014/entries/holes/ , title=The Stanford Encyclopedia of Philosophy , author-first1=Roberto , author-last1=Casati , author-first2=Achille , author-last2=Varzi , editor-first=Edward N. , editor-last=Zalta , date=2018-12-18 , publisher=Metaphysics Research Lab, Stanford University , via=Stanford Encyclopedia of Philosophy "Photographic impressions of Beatle songs by Art Kane", ''

LIFE Life is a quality that distinguishes matter that has biological processes, such as signaling and self-sustaining processes, from that which does not, and is defined by the capacity for growth, reaction to stimuli, metabolism, energy ...

'', Vol. 65, No. 12 (1968-09-20), p. 67. {{Cite news , newspaper=

The Daily Mail The ''Daily Mail'' is a British daily Middle-market newspaper, middle-market Tabloid journalism, tabloid newspaper and online newspaper, news websitePeter Wilb"Paul Dacre of the Daily Mail: The man who hates liberal Britain", ''New Statesman ...

, title=Far & Near: The holes in our roads , date=1967-01-17 , page=7 , issue=21994 David Zeb Cook, Jean Rabe, Warren Spector, ''Dungeon Master Guide for the AD&D Game'' (1995), p. 235. {{cite journal , author-last1=Martínez-Aguayo , author-first1=Juan Carlos , author-last2=Lanfranco , author-first2=Renzo C. , author-last3=Arancibia , author-first3=Marcelo , author-last4=Sepúlveda , author-first4=Elisa , author-last5=Madrid , author-first5=Eva , title=Trypophobia: What Do We Know So Far? A Case Report and Comprehensive Review of the Literature , journal=Frontiers in Psychiatry , volume=9 , pages=15 , date=2018 , issn=1664-0640 , doi=10.3389/fpsyt.2018.00015 , pmc=5811467 , pmid=29479321 , doi-access=free{{CC-notice, cc=by4, url=https://www.frontiersin.org/articles/10.3389/fpsyt.2018.00015/full, author(s)=Juan Carlos Martínez-Aguay, Renzo C. Lanfranco, Marcelo Arancibia, Elisa Sepúlveda and Eva Madrid {{cite journal , author-last1=Le , author-first1=An T. D. , author-last2=Cole , author-first2=Geoff G. , author-last3=Wilkins , author-first3=Arnold J. , s2cid=42086559 , title=Assessment of trypophobia and an analysis of its visual precipitation , journal=

Quarterly Journal of Experimental Psychology The Experimental Psychology Society (EPS) is an academic society which facilitates research into experimental psychology and communication between experimental psychologists. It is based in the United Kingdom. The society was originally formed as ...

, doi=10.1080/17470218.2015.1013970 , pmid=25635930 , date=2015-01-30 , volume=68 , issue=11 , pages=2304–2322 {{cite book , author-last1=Milosevic , author-first1=Irena , author-last2=McCabe , author-first2=Randi E. , title=Phobias: The Psychology of Irrational Fear , publisher= ABC-CLIO , isbn=978-1-61069576-3 , date=2015 , pages=401–402 , access-date=2017-10-25 , url=https://books.google.com/books?id=1BfYBgAAQBAJ&q=trypophobia {{Cite web , url=https://en.oxforddictionaries.com/definition/plot_hole , archive-url=https://web.archive.org/web/20170907213709/https://en.oxforddictionaries.com/definition/plot_hole , url-status=dead , archive-date=7 September 2017 , title=plot hole {{! Definition of plot hole in English by Oxford Dictionaries , website=Oxford Dictionaries , access-date=2017-09-07 Blakey Vermeule, ''Why Do We Care about Literary Characters?'' (2010), p. 10. {{Cite web , title=Unicode: Miscellaneous Symbols and Pictographs , url=https://www.unicode.org/charts/nameslist/c_1F300.html , access-date=2018-08-20 {{Cite web , title=Emoji Version 1.0 , url=https://emojipedia.org/emoji-1.0/ , access-date=2018-08-20 {{Cite web , title=Emojipedia: Hole , url=https://emojipedia.org/hole/ , access-date=2018-08-20