The restriction of a function f:XYf: X \to Y to a subset UU of XX is simply the composite of ff and the inclusion function of UU:

Ui UXfY. U \stackrel{i_U}\to X \stackrel{f}\to Y .

It is often written as f U:UYf_{|U}: U \to Y, or a variation on that theme.

Created on July 24, 2009 21:57:45 by Toby Bartels (