A homeomorphism f of topological spacesMathworldPlanetmath is a continuousMathworldPlanetmathPlanetmath, bijectiveMathworldPlanetmathPlanetmath 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