Template:Short description 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 <math>M = [a, b]</math>, a closed interval, see the article Non-standard calculus.