Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. 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.