Domain (mathematical Analysis), Domain
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A domain is a geographic area controlled by a single person or organization. Domain may also refer to:


Law and human geography

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Demesne A demesne ( ) or domain was all the land retained and managed by a lord of the manor under the feudal system for his own use, occupation, or support. This distinguished it from land subinfeudation, sub-enfeoffed by him to others as sub-tenants. ...
, in English common law and other Medieval European contexts, lands directly managed by their holder rather than being delegated to subordinate managers * Domaine, a large parcel of land under single ownership, which would historically generate income for its owner. *
Eminent domain Eminent domain, also known as land acquisition, compulsory purchase, resumption, resumption/compulsory acquisition, or expropriation, is the compulsory acquisition of private property for public use. It does not include the power to take and t ...
, the right of a government to appropriate another person's property for public use * Private domain / Public domain, places defined under Jewish law where it is either permitted or forbidden to move objects on the Sabbath day *
Public domain The public domain (PD) consists of all the creative work to which no Exclusive exclusive intellectual property rights apply. Those rights may have expired, been forfeited, expressly Waiver, waived, or may be inapplicable. Because no one holds ...
, creative work to which no exclusive intellectual property rights apply * Territory (subdivision), a non-sovereign geographic area which has come under the authority of another government


Science

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Domain (biology) In biological taxonomy, a domain ( or ) (Latin: ''regio''), also dominion, superkingdom, realm, or empire, is the highest taxonomic rank of all organisms taken together. It was introduced in the three-domain system of taxonomy devised by Carl ...
, a taxonomic subdivision larger than a kingdom *
Domain of discourse In the formal sciences, the domain of discourse or universe of discourse (borrowing from the mathematical concept of ''universe'') is the set of entities over which certain variables of interest in some formal treatment may range. It is also ...
, the collection of entities of interest in logical analysis * High-field domain (physics) in semiconductors, also called Böer domain * Knowledge domain, knowledge within a certain discipline, often formalized as a terminology *
Magnetic domain A magnetic domain is a region within a magnetic material in which the magnetization is in a uniform direction. This means that the individual magnetic moments of the atoms are aligned with one another and they point in the same direction. When c ...
(physics), a region within a magnetic material which has uniform magnetization *
Protein domain In molecular biology, a protein domain is a region of a protein's Peptide, polypeptide chain that is self-stabilizing and that Protein folding, folds independently from the rest. Each domain forms a compact folded Protein tertiary structure, thre ...
(biology), a part of a protein that can exist independently of the rest of the protein chain * Social domain, a concept in sociology


Mathematics

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Domain (mathematical analysis) In mathematical analysis, a domain or region is a non-empty, connected, and open set in a topological space. In particular, it is any non-empty connected open subset of the real coordinate space or the complex coordinate space . A connected op ...
, an open connected set *
Domain (ring theory) In algebra, a domain is a nonzero ring in which implies or .Lam (2001), p. 3 (Sometimes such a ring is said to "have the zero-product property".) Equivalently, a domain is a ring in which 0 is the only left zero divisor (or equivalently, the o ...
, a non-trivial ring without left or right nonzero zero divisors **
Integral domain In mathematics, an integral domain is a nonzero commutative ring in which the product of any two nonzero elements is nonzero. Integral domains are generalizations of the ring of integers and provide a natural setting for studying divisibilit ...
, a non-trivial commutative ring without nonzero zero divisors *** Atomic domain, an integral domain in which every nonzero non-unit is a finite product of irreducible elements ***
Bézout domain In mathematics, a Bézout domain is an integral domain in which the sum of two principal ideals is also a principal ideal. This means that Bézout's identity holds for every pair of elements, and that every finitely generated ideal is principal. ...
, an integral domain in which the sum of two principal ideals is again a principal ideal ***
Euclidean domain In mathematics, more specifically in ring theory, a Euclidean domain (also called a Euclidean ring) is an integral domain that can be endowed with a Euclidean function which allows a suitable generalization of Euclidean division of integers. Th ...
, an integral domain which allows a suitable generalization of the Euclidean algorithm ***
Dedekind domain In mathematics, a Dedekind domain or Dedekind ring, named after Richard Dedekind, is an integral domain in which every nonzero proper ideal factors into a product of prime ideals. It can be shown that such a factorization is then necessarily un ...
, an integral domain in which every nonzero proper ideal factors into a product of prime ideals ***
GCD domain In mathematics, a GCD domain (sometimes called just domain) is an integral domain ''R'' with the property that any two elements have a greatest common divisor (GCD); i.e., there is a unique minimal principal ideal containing the ideal generated ...
, an integral domain in which every two non-zero elements have a greatest common divisor ***
Principal ideal domain In mathematics, a principal ideal domain, or PID, is an integral domain (that is, a non-zero commutative ring without nonzero zero divisors) in which every ideal is principal (that is, is formed by the multiples of a single element). Some author ...
, an integral domain in which every ideal is principal ***
Unique factorization domain In mathematics, a unique factorization domain (UFD) (also sometimes called a factorial ring following the terminology of Bourbaki) is a ring in which a statement analogous to the fundamental theorem of arithmetic holds. Specifically, a UFD is ...
, an integral domain in which every non-zero element can be written as a product of irreducible elements in essentially a unique way *
Domain of a function In mathematics, the domain of a function is the Set (mathematics), set of inputs accepted by the Function (mathematics), function. It is sometimes denoted by \operatorname(f) or \operatornamef, where is the function. In layman's terms, the doma ...
, the set of input values for which the (total) function is defined **
Domain of definition In mathematics, a partial function from a set to a set is a function from a subset of (possibly the whole itself) to . The subset , that is, the '' domain'' of viewed as a function, is called the domain of definition or natural domain of ...
of a partial function **
Natural domain In mathematics, a partial function from a set to a set is a function from a subset of (possibly the whole itself) to . The subset , that is, the '' domain'' of viewed as a function, is called the domain of definition or natural domain of ...
of a partial function **
Domain of holomorphy In mathematics, in the theory of functions of several complex variables, a domain of holomorphy is a domain which is maximal in the sense that there exists a holomorphic function on this domain which cannot be extended to a bigger domain. Forma ...
of a function * Domain of an
algebraic structure In mathematics, an algebraic structure or algebraic system consists of a nonempty set ''A'' (called the underlying set, carrier set or domain), a collection of operations on ''A'' (typically binary operations such as addition and multiplicatio ...
, the set on which the algebraic structure is defined *
Domain of discourse In the formal sciences, the domain of discourse or universe of discourse (borrowing from the mathematical concept of ''universe'') is the set of entities over which certain variables of interest in some formal treatment may range. It is also ...
, the set of entities over which logic variables may range *
Domain theory Domain theory is a branch of mathematics that studies special kinds of partially ordered sets (posets) commonly called domains. Consequently, domain theory can be considered as a branch of order theory. The field has major applications in computer ...
, the study of certain subsets of continuous lattices that provided the first denotational semantics of the lambda calculus *
Frequency domain In mathematics, physics, electronics, control systems engineering, and statistics, the frequency domain refers to the analysis of mathematical functions or signals with respect to frequency (and possibly phase), rather than time, as in time ser ...
, the analysis of mathematical functions with respect to frequency, rather than time *
Fundamental domain Given a topological space and a group acting on it, the images of a single point under the group action form an orbit of the action. A fundamental domain or fundamental region is a subset of the space which contains exactly one point from each ...
, subset of a space that contains exactly one point from each orbit of the action of a symmetry group *
Time domain In mathematics and signal processing, the time domain is a representation of how a signal, function, or data set varies with time. It is used for the analysis of mathematical functions, physical signals or time series of economic or environmental ...
, the analysis of mathematical functions with respect to time


Information technology

* Administrative domain *
Broadcast domain A broadcast domain is a logical division of a computer network, in which all nodes can reach each other by broadcast at the data link layer. A broadcast domain can be within the same LAN segment or it can be bridged to other LAN segments. In te ...
, in computer networking, a group of special-purpose addresses to receive network announcements * Collision domain *
Domain (software engineering) In software engineering, domain is the targeted subject area of a computer program. Formally it represents the target subject of a specific programming project, whether narrowly or broadly defined. For example, for a particular programming projec ...
, a field of study that defines a set of common requirements, terminology, and functionality for any software program constructed to solve a problem in a given field **
Application domain An application domain is a mechanism (similar to a process in an operating system) used within the Common Language Infrastructure (CLI) to isolate executed software applications from one another so that they do not affect each other. Each applicat ...
, a mechanism used within a Common Language Infrastructure to isolate executed software applications from one another ** Programming domain, a set of programming languages or programming environments that were engineered specifically for a particular domain (software engineering) * Network domain, a named grouping of hosts and servers with managed login, access to resources, and permissions. **
Domain name In the Internet, a domain name is a string that identifies a realm of administrative autonomy, authority, or control. Domain names are often used to identify services provided through the Internet, such as websites, email services, and more. ...
, a label that identifies a realm of administrative autonomy, authority, or control within the Internet * Attribute domain, the set of values allowed in an attribute.


Places

* The Domain (Austin, Texas), a shopping mall in Austin, Texas, United States * Domain (Hong Kong shopping centre), a shopping mall in Yau Tong, Kowloon, Hong Kong * Domain, Manitoba, a hamlet in Manitoba, Canada * Domain Precinct, a part of South Yarra in Melbourne, Victoria, Australia


Australian public domains

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The Domain, Sydney The Domain is a heritage-listed area of open space on the eastern fringe of the Sydney central business district, Australia. Separating the central business district from Woolloomooloo, New South Wales, Woolloomooloo, The Domain adjoins the Ro ...
, a large open space near the central business district of Sydney * Kings Domain, Melbourne, Victoria *
Queens Domain The Queens Domain, also known as The Domain to locals, is an expansive area of bushland, parkland, and cultural sites located just north-east of the Hobart City Centre, bordering the Derwent River, Tasmania, River Derwent in the state capital ...
, Hobart, Tasmania


New Zealand public domains

* Auckland Domain: a large inner-city park in Auckland * One Tree Hill Domain in Auckland * Mount Eden Domain in Auckland * Mount Smart Domain in Auckland * Mangere Domain in Mangere * Hamilton Lake Domain in Hamilton * Taumarunui Domain in Taumarunui * Ashburton Domain in Canterbury * Ocean Beach Domain in Dunedin


Entertainment


Film

* ''Domain'' (2009 film), a French film * ''Domain'' (2016 film), an American film * ''The Domain'' (film), a 2019 Portuguese film


Music

* "Domain", track by John Carpenter from Lost Themes * "Domain", a song by KSI from the 2020 album ''Dissimulation''


Other uses

* Domain, or
battlespace Battlespace or battle-space is a term used to signify a military strategy which integrates multiple armed forces for the military theater (warfare), theatre of operations, including aerial warfare, air, information warfare, information, ground w ...
, a concept in military operations dividing operating environments into defined components * Domain Group, an Australian real estate marketing portal, owner of the brand domain.com.au and others


See also

* Dominion (disambiguation) {{Disambiguation, geo