Heine–Cantor theorem should not be confused with Cantor's theorem.
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]