Extension, extend or extended may refer to:

Mathematics

Logic or set theory

Axiom of extensionality In axiomatic set theory and the branches of logic, mathematics, and computer science that use it, the axiom of extensionality, or axiom of extension, is one of the axioms of Zermelo–Fraenkel set theory. It says that sets having the same elements ...

* Extensible cardinal * Extension (model theory) *

Extension (predicate logic) The extension of a predicatea truth-valued functionis the set of tuples of values that, used as arguments, satisfy the predicate. Such a set of tuples is a relation. Examples For example, the statement "''d2'' is the weekday following ''d1''" can ...

, the set of tuples of values that satisfy the predicate *

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 *

Extension by definitions In mathematical logic, more specifically in the proof theory of first-order theories, extensions by definitions formalize the introduction of new symbols by means of a definition. For example, it is common in naive set theory to introduce a symbol ...

Extensional definition In logic, extensional and intensional definitions are two key ways in which the objects, concepts, or referents a term refers to can be defined. They give meaning or denotation to a term. Intensional definition An intensional definition gives m ...

, a definition that enumerates every individual a term applies to *

Extensionality In logic, extensionality, or extensional equality, refers to principles that judge objects to be equal if they have the same external properties. It stands in contrast to the concept of intensionality, which is concerned with whether the internal ...

Other uses

Extension of a polyhedron In convex geometry and polyhedral combinatorics, the extension complexity is a convex polytope P is the smallest number of facets among convex polytopes Q that have P as a projection. In this context, Q is called an extended formulation of P; it m ...

, in geometry *

Exterior algebra In mathematics, the exterior algebra, or Grassmann algebra, named after Hermann Grassmann, is an algebra that uses the exterior product or wedge product as its multiplication. In mathematics, the exterior product or wedge product of vectors is ...

, Grassmann's theory of extension, in geometry *

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 dual ...

, in topology *

Kolmogorov extension theorem In mathematics, the Kolmogorov extension theorem (also known as Kolmogorov existence theorem, the Kolmogorov consistency theorem or the Daniell-Kolmogorov theorem) is a theorem that guarantees that a suitably "consistent" collection of finite-di ...

, in probability theory *

Linear extension In order theory, a branch of mathematics, a linear extension of a partial order is a total order (or linear order) that is compatible with the partial order. As a classic example, the lexicographic order of totally ordered sets is a linear extens ...

, in order theory *

Sheaf extension In mathematics, a sheaf of ''O''-modules or simply an ''O''-module over a ringed space (''X'', ''O'') is a sheaf ''F'' such that, for any open subset ''U'' of ''X'', ''F''(''U'') is an ''O''(''U'')-module and the restriction maps ''F''(''U'') � ...

, in algebraic geometry *

Tietze extension theorem In topology, the Tietze extension theorem (also known as the Tietze–Urysohn–Brouwer extension theorem) states that continuous functions on a closed subset of a normal topological space can be extended to the entire space, preserving boundedness ...

, in topology *

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 e ...

, in differential geometry *

Group extension In mathematics, a group extension is a general means of describing a group in terms of a particular normal subgroup and quotient group. If Q and N are two groups, then G is an extension of Q by N if there is a short exact sequence :1\to N\;\overs ...

, in abstract algebra and homological algebra

Music

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, for exam ...

, notes that fit outside the standard range * ''Extended'' (Solar Fields album), 2005 * ''Extension'' (George Braith album), 1964 * ''Extension'' (Clare Fischer album), 1963 * ''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 ...

* ''Extensions'' (McCoy Tyner album), 1970 * ''Extensions'' (Dave Holland album), 1988 * ''Extensions'' (The Manhattan Transfer album), 1979

Places

Extension, British Columbia Extension is an unincorporated community near the east coast of southern Vancouver Island, British Columbia. The location off BC Highway 19 is about by road northwest of Victoria, and south of Nanaimo. Discovery Louis Stark, an African American ...

, a village near Regional District of Nanaimo, British Columbia, Canada *

Extension, Louisiana Extension is an unincorporated community in Franklin Parish, Louisiana, United States. Its ZIP code is 71243. Notable people Singer and songwriter Richard Berry was born in Extension. He is known for writing one of the world's most recorded song ...

, unincorporated community, United States

Science

Extension (geology) Extensional tectonics is concerned with the structures formed by, and the tectonic processes associated with, the stretching of a planetary body's crust or lithosphere. Deformation styles The types of structure and the geometries formed depend on ...

, relating to the pulling apart of the Earth's crust and lithosphere *

Extension (anatomy) Motion, the process of movement, is described using specific anatomical terms. Motion includes movement of organs, joints, limbs, and specific sections of the body. The terminology used describes this motion according to its direction relativ ...

, 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 terms. Motion includes movement of organs, joints, limbs, and specific sections of the body. The terminology used describes this motion according to its direction relative ...

* Extension locus, the gene locus of

Melanocortin 1 receptor The melanocortin 1 receptor (MC1R), also known as melanocyte-stimulating hormone receptor (MSHR), melanin-activating peptide receptor, or melanotropin receptor, is a G protein–coupled receptor that binds to a class of pituitary peptide hormones ...

Other uses

Browser extension A browser extension is a small software module for customizing a web browser. Browsers typically allow a variety of extensions, including user interface modifications, cookie management, ad blocking, and the custom scripting and styling of web p ...

, a small software module for customizing a web browser * Building extension *

Continuing education Continuing education (similar to further education in the United Kingdom and Republic of Ireland, Ireland) is an all-encompassing term within a broad list of post-secondary learning activities and programs. The term is used mainly in the United ...

, or extension school, a school for continuing education *

Cooperative State Research, Education, and Extension Service The Cooperative State Research, Education, and Extension Service (CSREES) was an extension agency within the U.S. Department of Agriculture (USDA), part of the executive branch of the federal government. The 1994 Department Reorganization Act, ...

, a former division of the U.S. Department of Agriculture *

Extension (metaphysics) In metaphysics, extension signifies both 'stretching out' (Latin: ''extensio'') as well as later 'taking up space', and most recently, spreading one's internal mental cognition into the external world. The history of thinking about ''extension'' ca ...

, the property of stretching out or taking up space *

Extension (telephone) In residential telephony, an extension telephone is an additional telephone wired to the same telephone line as another. In middle 20th century telephone jargon, the first telephone on a line was a "Main Station" and subsequent ones "Extensions" o ...

, telephone line attached to a main line or to a PBX or Centrex system *

Extension cord An extension cord (US), power extender, drop cord, or extension lead (UK) is a length of flexible electrical power cable (flex) with a AC power plugs and sockets, plug on one end and one or more sockets on the other end (usually of the same type ...

, power cable with a plug on one end and one or more sockets on the other end *

Eyelash extensions Eyelash extensions are a cosmetics, cosmetic enhancement that involves attaching synthetic or natural hair fibers to the natural Eyelash, eyelashes to create a fuller, more dramatic look. They are applied by a professional using a specialized adhe ...

, material applied to eyelashes *

Hair extensions Artificial hair integrations, more commonly known as hair extensions, hair weaves, and fake hair add length and fullness to human hair. Hair extensions are usually clipped, glued, or sewn on natural hair by incorporating additional human or syn ...

, strands of hair added to existing hair * Extension, the building of community capacity by outsiders, for instance

agricultural extension Agricultural extension is the application of scientific research and new knowledge to agricultural practices through farmer education. The field of 'extension' now encompasses a wider range of communication and learning activities organized for r ...

Filename extension A filename extension, file name extension or file extension is a suffix to the name of a computer file (e.g., .txt, .docx, .md). The extension indicates a characteristic of the file contents or its intended use. A filename extension is typically d ...

, for computer file systems

Mathematics

Logic or set theory

Other uses

Music

Places

Science

Other uses

See also