Extension, extend or extended may refer to:
Mathematics
Logic or set theory
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Axiom of extensionality
The axiom of extensionality, also called the axiom of extent, is an axiom used in many forms of axiomatic set theory, such as Zermelo–Fraenkel set theory. The axiom defines what a Set (mathematics), set is. Informally, the axiom means that the ...
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Extensible cardinal
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Extension (model theory)
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Extension (proof theory)
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Extension (predicate logic), the set of tuples of values that satisfy the predicate
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Extension (semantics)
In any of several fields of study that treat the use of signs — for example, in linguistics, logic, mathematics, semantics, semiotics, and philosophy of language — the extension of a concept, idea, or sign consists of the things to which it ap ...
, the set of things to which a property applies
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Extension (simplicial set)
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Extension by definitions
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Extensional definition, a definition that enumerates every individual a term applies to
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Extensionality
Other uses
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Extension of a function, defined on a larger domain
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Extension of a polyhedron, in geometry
* Extension of a
line segment
In geometry, a line segment is a part of a line (mathematics), straight line that is bounded by two distinct endpoints (its extreme points), and contains every Point (geometry), point on the line that is between its endpoints. It is a special c ...
(finite) into an infinite line (e.g.,
extended base)
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Exterior algebra
In mathematics, the exterior algebra or Grassmann algebra of a vector space V is an associative algebra that contains V, which has a product, called exterior product or wedge product and denoted with \wedge, such that v\wedge v=0 for every vector ...
, Grassmann's theory of extension, in geometry
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Field extension
In mathematics, particularly in algebra, a field extension is a pair of fields K \subseteq L, such that the operations of ''K'' are those of ''L'' restricted to ''K''. In this case, ''L'' is an extension field of ''K'' and ''K'' is a subfield of ...
, in Galois theory
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Group extension, in abstract algebra and homological algebra
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Homotopy extension property
In mathematics, in the area of algebraic topology, the homotopy extension property indicates which homotopies defined on a subspace can be extended to a homotopy defined on a larger space. The homotopy extension property of cofibrations is du ...
, in topology
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Kolmogorov extension theorem, in probability theory
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Linear extension, in order theory
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Sheaf extension, in algebraic geometry
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Tietze extension theorem
In topology, the Tietze extension theorem (also known as the Tietze– Urysohn– Brouwer extension theorem or Urysohn-Brouwer lemma) states that any real-valued, continuous function on a closed subset of a normal topological space
In mathe ...
, in topology
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Whitney extension theorem
In mathematics, in particular in mathematical analysis, the Whitney extension theorem is a partial converse to Taylor's theorem. Roughly speaking, the theorem asserts that if ''A'' is a closed subset of a Euclidean space, then it is possible to ...
, in differential geometry
Music
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Extension (music)
In music, an extension is a set of musical notes that lie outside the standard range or tessitura.
Staff
A note that lies outside the lines of a musical staff is an extension of the staff. The note will lie on a ledger line. Middle C, f ...
, notes that fit outside the standard range
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''Extended'' (Solar Fields album), 2005
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''Extension'' (George Braith album), 1964
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''Extension'' (Clare Fischer album), 1963
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''Extensions'' (Ahmad Jamal album), 1965
* ''Extensions'', a 1969 album by
Mystic Moods Orchestra
The Mystic Moods Orchestra was a group known for mixing orchestral pop, environmental sounds, and pioneering recording techniques. It was created by audiophile Brad Miller. The first Mystic Moods Orchestra album, ''One Stormy Night'', was released ...
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''Extensions'' (McCoy Tyner album), 1970
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''Extensions'' (Dave Holland album), 1988
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''Extensions'' (The Manhattan Transfer album), 1979
* Extension (The Extended Mixes), 2023 album reissue by
Kylie Minogue
Kylie Ann Minogue (; born 28 May 1968) is an Australian singer, songwriter, and actress. Frequently referred to as the "Honorific nicknames in popular music, Princess of Pop", she has achieved recognition in both the music industry and fas ...
Places
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Extension, British Columbia, a village near Regional District of Nanaimo, British Columbia, Canada
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Extension, Louisiana
Extension is an Unincorporated area#United States, unincorporated community in Franklin Parish, Louisiana, Franklin Parish, Louisiana, United States. Its ZIP code is 71243.
Notable people
Singer and songwriter Richard Berry (musician), Richard Be ...
, unincorporated community, United States
Science
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Extension (geology)
Extensional tectonics is concerned with the structures formed by, and the Tectonics, tectonic processes associated with, the stretching of a planetary body's Crust (geology), crust or lithosphere.
Deformation styles
The types of structure and the ...
, relating to the pulling apart of the Earth's crust and lithosphere
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Extension (anatomy), a movement at a
joint
A joint or articulation (or articular surface) is the connection made between bones, ossicles, or other hard structures in the body which link an animal's skeletal system into a functional whole.Saladin, Ken. Anatomy & Physiology. 7th ed. McGraw- ...
that increases the angle between the two ends of the joint; the opposite of
flexion
Motion, the process of movement, is described using specific anatomical terminology, anatomical terms. Motion includes movement of Organ (anatomy), organs, joints, Limb (anatomy), limbs, and specific sections of the body. The terminology used de ...
* Extension locus, the gene locus of
Melanocortin 1 receptor
Other uses
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Agricultural Extension
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Browser extension
A browser extension is a software module for customizing a web browser. Browsers typically allow users to install a variety of extensions, including user interface modifications, cookie management, ad blocking, and the custom scripting and st ...
, a small software module for customizing a web browser
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Building extension
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Continuing education
Continuing education is the education undertaken after initial education for either personal or professional reasons. The term is used mainly in the United States and Canada.
Recognized forms of post-secondary learning activities within the d ...
, or extension school, a school for continuing education
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Cooperative State Research, Education, and Extension Service, a former division of the U.S. Department of Agriculture
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Extension (metaphysics), the property of stretching out or taking up space
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Extension (telephone), telephone line attached to a main line or to a PBX or Centrex system
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Extension cord, power cable with a plug on one end and one or more sockets on the other end
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Eyelash extensions, material applied to eyelashes
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Hair extensions, strands of hair added to existing hair
* Extension, the building of community capacity by outsiders, for instance
agricultural extension
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Filename extension
A filename extension, file name extension or file extension is a suffix to the name of a computer file (for example, .txt, .mp3, .exe) that indicates a characteristic of the file contents or its intended use. A filename extension is typically d ...
, for computer file systems
See also
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Extensive (disambiguation)
{{Disambiguation