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restriction of a function
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(Definition)
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Let $f\colon X\to Y$ be a function from a set $X$ to a set $Y$ If $A$ is a subset of $X$ then the <</SPAN>#45#>restriction of $f$ to $A$ is the function \begin{eqnarray*} f|_A\colon A&\to& Y \\ x&\mapsto& f(x). \end{eqnarray*}Some authors write $f\upharpoonright A$ instead of $f|_A$
If $A\subseteq X$ and $B\subseteq Y$ then \begin{eqnarray*} (f|_A)^{-1}(B)&=&A\cap f^{-1}(B). \end{eqnarray*}
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"restriction of a function" is owned by yark. [ full author list (3) | owner history (2) ]
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Cross-references: subset, function
There are 15 references to this entry.
This is version 11 of restriction of a function, born on 2003-06-26, modified 2008-04-26.
Object id is 4401, canonical name is RestrictionOfAFunction.
Accessed 13105 times total.
Classification:
| AMS MSC: | 03E20 (Mathematical logic and foundations :: Set theory :: Other classical set theory ) |
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Pending Errata and Addenda
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