# Restriction

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Please note that this does not mean the content is unreliable, it just means that the author of the page doesn't have a book to hand, or remember the book to find it, which would have been a suitable reference.

## Definition

Given a map, [ilmath]f:X\rightarrow Y[/ilmath] for sets, [ilmath]X[/ilmath] and [ilmath]Y[/ilmath], and given any [ilmath]A\in\mathcal{P}(X)[/ilmath][Note 1] (so [ilmath]A\subseteq X[/ilmath] - and is any subset) we define a new function, the restriction of [ilmath]f[/ilmath] to [ilmath]A[/ilmath] as:

• [ilmath]f\vert_A:A\rightarrow Y[/ilmath] by [ilmath]f\vert_A:a\mapsto f(a)[/ilmath]

TODO: These