## You are here

Homehomeomorphism

## Primary tabs

# 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.

Defines:

homeomorphic, autohomeomorphism, auto-homeomorphism, self-homeomorphism

Related:

Homeotopy, CrosscapSlide, AlexanderTrick, GroupoidCategory

Synonym:

topological equivalence, topologically equivalent

Type of Math Object:

Definition

Major Section:

Reference

## Mathematics Subject Classification

54C05*no label found*

- Forums
- Planetary Bugs
- HS/Secondary
- University/Tertiary
- Graduate/Advanced
- Industry/Practice
- Research Topics
- LaTeX help
- Math Comptetitions
- Math History
- Math Humor
- PlanetMath Comments
- PlanetMath System Updates and News
- PlanetMath help
- PlanetMath.ORG
- Strategic Communications Development
- The Math Pub
- Testing messages (ignore)

- Other useful stuff

## Recent Activity

Sep 14

new problem: Geometry by parag

Aug 24

new question: Scheduling Algorithm by ncovella

new question: Scheduling Algorithm by ncovella

new problem: Geometry by parag

Aug 24

new question: Scheduling Algorithm by ncovella

new question: Scheduling Algorithm by ncovella

## Attached Articles

## Corrections

Topolgical equivalence by rspuzio ✓

self-homeomorphism by yark ✓

typo by yark ✓

another typo by yark ✓

typo by yark ✓

self-homeomorphism by yark ✓

typo by yark ✓

another typo by yark ✓

typo by yark ✓