Heine-Cantor theorem

Let $X,Y$ be uniform spaces, and $f:X\to Y$ a continuous function. If $X$ is compact, then $f$ is uniformly continuous.

For instance, if $f:[a,b]\to ℝ$ 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