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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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## Recent Activity

Oct 21

new question: Prime numbers out of sequence by Rubens373

Oct 7

new question: Lorenz system by David Bankom

Oct 19

new correction: examples and OEIS sequences by fizzie

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new correction: Define Galois correspondence by porton

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new correction: Closure properties on languages: DCFL not closed under reversal by babou

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new correction: Many corrections by Smarandache

Sep 28

new question: how to contest an entry? by zorba

new question: simple question by parag

new question: Prime numbers out of sequence by Rubens373

Oct 7

new question: Lorenz system by David Bankom

Oct 19

new correction: examples and OEIS sequences by fizzie

Oct 13

new correction: Define Galois correspondence by porton

Oct 7

new correction: Closure properties on languages: DCFL not closed under reversal by babou

new correction: DCFLs are not closed under reversal by petey

Oct 2

new correction: Many corrections by Smarandache

Sep 28

new question: how to contest an entry? by zorba

new question: simple question by parag

## Comments

## uniform space

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