Heine-Cantor theorem

Let X,Y be uniform spaces, and f:XY a continuous functionMathworldPlanetmathPlanetmath. If X is compactPlanetmathPlanetmath, then f is uniformly continuousPlanetmathPlanetmath.

For instance, if f:[a,b] is a continuous function, then it is uniformly continuous.

Title Heine-Cantor theorem
Canonical name HeineCantorTheorem
Date of creation 2013-03-22 12:45:32
Last modified on 2013-03-22 12:45:32
Owner n3o (216)
Last modified by n3o (216)
Numerical id 9
Author n3o (216)
Entry type Theorem
Classification msc 46A99