inverse function theorem (topological spaces)

Let X and Y be topological spacesMathworldPlanetmath, with X compactPlanetmathPlanetmath and Y HausdorffPlanetmathPlanetmath. Suppose f:XY is a continuousPlanetmathPlanetmath bijection. Then f is a homeomorphismPlanetmathPlanetmath, i.e. f-1 is continuous.

Note if Y is a metric space, then it is Hausdorff, and the theorem holds.

Title inverse function theorem (topological spaces)
Canonical name InverseFunctionTheoremtopologicalSpaces
Date of creation 2013-03-22 13:25:04
Last modified on 2013-03-22 13:25:04
Owner mathcam (2727)
Last modified by mathcam (2727)
Numerical id 9
Author mathcam (2727)
Entry type Theorem
Classification msc 54C05
Related topic Compact