Homeomorphism

From Conservapedia

A homeomorphism is a continuous function f with a continuous inverse mapping a topological space X to a topological space Y such that f(f^-1) is the identity function on X; X and Y are then said to be homeomorphic. A homeomorphism establishes a bijective correspondence between the collection of open sets in X and Y.

Important Theorem: If there exist a continuous bijection from a compact space X to a Hausdorff space Y, then X and Y are homeomorphic.

Homeomorphic spaces are indistinguishable in topology. An example of such indistinguishable spaces are a coffee cup and a donut. These are topologically equivalent because they are both solid three-dimensional objects with one hole through them.