# homeomorphism

A homeomorphism $f$ of topological spaces is a continuous, bijective map such that $f^{-1}$ is also continuous. We also say that two spaces are homeomorphic if such a map exists.

If two topological spaces are homeomorphic, they are topologically equivalent — using the techniques of topology, there is no way of distinguishing one space from the other.

An autohomeomorphism (also known as a self-homeomorphism) is a homeomorphism from a topological space to itself.

 Title homeomorphism Canonical name Homeomorphism Date of creation 2013-03-22 11:59:35 Last modified on 2013-03-22 11:59:35 Owner rspuzio (6075) Last modified by rspuzio (6075) Numerical id 16 Author rspuzio (6075) Entry type Definition Classification msc 54C05 Synonym topological equivalence Synonym topologically equivalent Related topic Homeotopy Related topic CrosscapSlide Related topic AlexanderTrick Related topic GroupoidCategory Defines homeomorphic Defines autohomeomorphism Defines auto-homeomorphism Defines self-homeomorphism