Editing Continuous function (section)

===Homeomorphisms===
Symmetric to the concept of a continuous map is an [[open map]], for which {{em|images}} of open sets are open. If an open map ''f'' has an [[inverse function]], that inverse is continuous, and if a continuous map ''g'' has an inverse, that inverse is open. Given a [[bijective]] function ''f'' between two topological spaces, the inverse function <math>f^{-1}</math> need not be continuous. A bijective continuous function with a continuous inverse function is called a {{em|[[homeomorphism]]}}.

If a continuous bijection has as its [[Domain of a function|domain]] a [[compact space]] and its codomain is [[Hausdorff space|Hausdorff]], then it is a homeomorphism.