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, $f:X\rightarrow Y$ for sets, $X$ and $Y$, and given any $A\in\mathcal{P}(X)$ (so $A\subseteq X$ - and is any subset) we define a new function, the restriction of $f$ to $A$ as:

• $f\vert_A:A\rightarrow Y$ by $f\vert_A:a\mapsto f(a)$

To-do

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TODO: These

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1. Link with inclusion mapping