Definition

Let $f\colon X\to Y$ be a function from a set

to a set

. If

is a subset of

, then the restriction of

is the function

$\displaystyle f\vert _A\colon A$	$\displaystyle \to$	$\displaystyle Y$
$\displaystyle x$	$\displaystyle \mapsto$	$\displaystyle f(x).$

Some authors write $f\upharpoonright A$ instead of $f\vert _A$ .

Properties

If $A\subseteq X$ , and $B\subseteq Y$ , then

$\displaystyle (f\vert _A)^{-1}(B)$

$\displaystyle =$

$\displaystyle A\cap f^{-1}(B).$

"restriction of a function" is owned by yark. [ full author list (3) | owner history (2) ]

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Other names:

restriction

This object's parent.

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Cross-references: subset, function
There are 34 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 10439 times total.

Classification:

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

Pending Errata and Addenda

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