extension of a function
Let f:X→Y be a function and A and B be sets such that X⊆A and Y⊆B. An extension of f to A is a function g:A→B such that f(x)=g(x) for all x∈X. Alternatively, g is an extension of f to A if f is the restriction of g to X.
Typically, functions are not arbitrarily extended. Rather, it is usually insisted upon that extensions have certain properties. Examples include analytic continuations and meromorphic extensions.
Title | extension of a function |
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Canonical name | ExtensionOfAFunction |
Date of creation | 2013-03-22 17:51:00 |
Last modified on | 2013-03-22 17:51:00 |
Owner | Wkbj79 (1863) |
Last modified by | Wkbj79 (1863) |
Numerical id | 6 |
Author | Wkbj79 (1863) |
Entry type | Definition |
Classification | msc 03E20 |
Related topic | RestrictionOfAFunction |
Defines | extension |