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 ahomeomorphism 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