In topology, an open map is a function between two topological spaces which maps open sets to open sets. Since open sets fundamentally describe topological spaces, these maps preserve many important properties.
If an open map has an inverse, that is if it's injective, then its inverse is continuous. If an open map is also a continuous bijection, then it is a homeomorphism. Put another way, a bijection is a homeomorphism if and only both it and its inverse are open maps.
