coercive function

Definition 1 (coercive function).

Let X and Y be topological spacesMathworldPlanetmath. A function f:XY is said to be coercive if for every compact set JY there exists a compact set KX such that


The general definition given above has a clear sense when specialized to the Euclidean spaces, as shown in the following result.

Proposition 1 (coercive functions on Rn).

A function f:RnRm is coercive if and only if

Title coercive function
Canonical name CoerciveFunction
Date of creation 2013-03-22 15:20:13
Last modified on 2013-03-22 15:20:13
Owner paolini (1187)
Last modified by paolini (1187)
Numerical id 5
Author paolini (1187)
Entry type Definition
Classification msc 54A05
Synonym coercive
Synonym coercitive
Synonym coercitive function