CentralNotice Homeomorphism From Wikipedia, the free encyclopedia Jump to: navigation , search Not to be confused with homomorphism . For homeomorphisms in graph theory, see homeomorphism (graph theory) . "Topological equivalence" redirects here. For topological equivalence in dynamical systems, see Topological conjugacy . A continuous deformation between a coffee mug and a donut ( torus ) illustrating that they are homeomorphic. But there need not be a continuous deformation for two spaces to be homeomorphic — only a continuous mapping with a continuous inverse. In the mathematical field of topology , a homeomorphism or topological isomorphism or bi continuous function is a continuous function between topological spaces that has a continuous inverse function . Homeomorphisms are the isomorphisms in the category of topological spaces —that is, they are the mapping...