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:
- f is a bijection.
- f is continuous.
- 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.