What is Heine–Cantor theorem?

In mathematics, the Heine–Cantor theorem, named after Eduard Heine and Georg Cantor, states that if f : M → N {\displaystyle f\colon M\to N} is a continuous function between two metric spaces M {\displaystyle M} and N {\displaystyle N} , and M {\displaystyle M} is compact, then f {\displaystyle f} is uniformly continuous. An important special case is that every continuous function from a closed bounded interval to the real numbers is uniformly continuous.