Extension

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Extension, extend or extended may refer to:

Mathematics

Logic or set theory

• Axiom of extensionality
• Extensible cardinal
• Extension (model theory)
• Extension (proof theory)
• Extension (predicate logic), the set of tuples of values that satisfy the predicate
• Extension (semantics), the set of things to which a property applies
• Extension (simplicial set)
• Extension by definitions
• Extensional definition, a definition that enumerates every individual a term applies to
• Extensionality

Other uses

• Extension of a function, defined on a larger domain
• Extension of a polyhedron, in geometry
• Extension of a line segment (finite) into an infinite line (e.g., extended base)
• Exterior algebra, Grassmann's theory of extension, in geometry
• Field extension, in Galois theory
• Group extension, in abstract algebra and homological algebra
• Homotopy extension property, in topology
• Kolmogorov extension theorem, in probability theory
• Linear extension, in order theory
• Sheaf extension, in algebraic geometry
• Tietze extension theorem, in topology
• Whitney extension theorem, in differential geometry

Music

• Extension (music), 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), 1960
• Extensions, a 1969 album by Mystic Moods Orchestra
• Extensions (McCoy Tyner album), 1970
• Extensions (Dave Holland album), 1988
• Extensions (The Manhattan Transfer album), 1979
• Extension (The Extended Mixes), 2023 album reissue by Kylie Minogue

Places

• Extension, British Columbia, a village near Regional District of Nanaimo, British Columbia, Canada
• Extension, Louisiana, unincorporated community, United States

Science

• Extension (geology), relating to the pulling apart of the Earth's crust and lithosphere
• Extension (anatomy), a movement at a joint that increases the angle between the two ends of the joint; the opposite of flexion
• Extension locus, the gene locus of Melanocortin 1 receptor

Other uses

• Agricultural extension service
  • Cooperative State Research, Education, and Extension Service, a former division of the U.S. Department of Agriculture
• Extension, the building of community capacity by outsiders, for instance agricultural extension
• Plug-in (computing), a software component that adds a specific feature to an existing computer program
• Browser extension, a small software module for customizing a web browser
• Building extension
• Continuing education, or extension school, a school for continuing education
• Extension (metaphysics), the property of stretching out or taking up space
• Extension (telephone), telephone line attached to a main line or to a PBX or Centrex system
• Extension cord, power cable with a plug on one end and one or more sockets on the other end
• Eyelash extensions, material applied to eyelashes
• Hair extensions, strands of hair added to existing hair
• Filename extension, for computer file systems

See also

• Extensive (disambiguation)