High Quality Content by WIKIPEDIA articles! In mathematics, the Heine–Cantor theorem, named after Eduard Heine and Georg Cantor, states that if M is a compact metric space, then every continuous function f : M ? N,where N is a metric space, is uniformly continuous. For instance, if f : [a,b] ? R is a continuous function, then it is uniformly continuous. For an alternative proof in the case of M = [a,b] a closed interval, see the article on non-standard calculus.

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