That is, a homeomorphism is a continuous map of topological spaces such that there is an inverse that is also a continuous map of topological spaces. Equivalently, is a bijection between the underlying sets such that both and its inverse are continuous.
Note that a continous bijection is not necessarily a homeomorphism; that is, is not a balanced category.
The term ‘homeomorphism’ is also applied to isomorphisms in categories that generalise , such as the category of convergence spaces and the category of locales.
Revised on May 24, 2010 10:05:52
by Urs Schreiber