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[parent] extension of a function (Definition)

Let $ f\colon X \to Y$ be a function and $ A$ and $ B$ be sets such that $ X\subseteq A$ and $ Y\subseteq B$. An extension of $ f$ to $ A$ is a function $ g\colon A \to B$ such that $ f(x)=g(x)$ for all $ x\in 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.



"extension of a function" is owned by Wkbj79.
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See Also: restriction of a function

Also defines:  extension

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Cross-references: meromorphic extensions, analytic continuations, properties, restriction, function
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This is version 3 of extension of a function, born on 2008-02-22, modified 2008-02-22.
Object id is 10322, canonical name is ExtensionOfAFunction.
Accessed 365 times total.

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AMS MSC: 03E20 (Mathematical logic and foundations :: Set theory :: Other classical set theory )
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