Heine–Cantor theorem

Template:DistinguishTemplate:No footnotes In mathematics, the Heine–Cantor theorem states that a continuous function between two metric spaces is uniformly continuous if its domain is compact. The theorem is named after Eduard Heine and Georg Cantor.

Template:Math theorem An important special case of the Cantor theorem is that every continuous function from a closed bounded interval to the real numbers is uniformly continuous.

For an alternative proof in the case of $M=[a,b]$, a closed interval, see the article Non-standard calculus.

See also

• Cauchy-continuous function

External links

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