Homeomorphism

A homeomorphism is a topological isomorphism. More precisely, suppose X and Y are topological spaces, and f is a function from X to Y. Then f is a homeomorphism iff all the following hold:

1. f is a bijection.
2. f is continuous.
3. f ^-1 is continuous.

If f : X -> Y is a homeomorphism, then Y is said to be homeomorphic to X (or to be a homeomorph of X). If two spaces are homeomorphic then they have exactly the same topological properties.