Extension (mathematics)

In mathematics, the word "extension" has many uses. See:

Analysis

* Carathéodory's extension theorem
* Continuous linear extension
* M. Riesz extension theorem
* Krein extension theorem
* Hahn-Banach theorem

Algebra

* Abelian extension
* Algebraic extension
* Artin-Schreier extension
* Central extension
* Cyclotomic extension—see abelian extension
* Degree of a field extension
* Dual basis in a field extension
* Extension problem
* Field extension
* Galois extension
* Group extension
* Integral extension
* Kernel extension theorem
* Kummer extension
* Normal extension
* Quadratic extension
* Quadratic field extension
* Ring extension
* Separable extension
* Simple extension
* Splitting of prime ideals in Galois extensions
* Trivial extension—see field extension

Algebraic geometry

* Sheaf extension

Logic / Set theory

* Axiom of extensionality
* Extensible cardinal
* Extension (model theory)
* Extension (predicate logic)
* Extensionality

Order theory

* Linear extension

Probability theory

* Kolmogorov extension theorem

Topology

* Homotopy extension property
* Tietze extension theorem

Geometry

* Exterior algebra, Grassmann's "theory of extension".


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