Restriction (mathematics)
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In mathematics, the notion of restriction finds a general definition in the context of sheaves.
Often, the following definition will be sufficient:
If f: E -> F is a (partial) function from E to F, and A is a subset of E, then the restriction of f to A is the (partial) function
having the graph 
.
(In rough words, it is "the same function", but only defined on 
.)
More generally, the restriction of a binary relation is usually defined in the same way. (One could also define a restriction to a subset of E x F, and the same applies to n-ary relations. These cases do not fit into the scheme of sheaves.)
[edit] Examples
- The restriction of the non injective function
to 
is the injection 
. - The canonical injection of a set A into a superset E of A.
