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.
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 ] {\displaystyle M=[a,b]} , a closed interval, see the article Non-standard calculus.
See also Cauchy-continuous function
External links Heine–Cantor theorem at PlanetMath. Proof of Heine–Cantor theorem at PlanetMath.