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# 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.

Type of Math Object:

Theorem

Major Section:

Reference

## Mathematics Subject Classification

46A99*no label found*

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## Comments

## uniform space

I believe R can be replaced by an arbitrary uniform space in this theorem.