# Heine-Cantor theorem

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

For instance, if $f:[a,b]\rightarrow\mathbb{R}$ is a continuous function, then it is uniformly continuous.

Title Heine-Cantor theorem HeineCantorTheorem 2013-03-22 12:45:32 2013-03-22 12:45:32 n3o (216) n3o (216) 9 n3o (216) Theorem msc 46A99