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Homehomeomorphism

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# 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*

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## Recent Activity

Oct 7

new question: Lorenz system by David Bankom

Oct 19

new correction: examples and OEIS sequences by fizzie

Oct 13

new correction: Define Galois correspondence by porton

Oct 7

new correction: Closure properties on languages: DCFL not closed under reversal by babou

new correction: DCFLs are not closed under reversal by petey

Oct 2

new correction: Many corrections by Smarandache

Sep 28

new question: how to contest an entry? by zorba

new question: simple question by parag

Sep 26

new question: Latent variable by adam_reith

new question: Lorenz system by David Bankom

Oct 19

new correction: examples and OEIS sequences by fizzie

Oct 13

new correction: Define Galois correspondence by porton

Oct 7

new correction: Closure properties on languages: DCFL not closed under reversal by babou

new correction: DCFLs are not closed under reversal by petey

Oct 2

new correction: Many corrections by Smarandache

Sep 28

new question: how to contest an entry? by zorba

new question: simple question by parag

Sep 26

new question: Latent variable by adam_reith

## 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 ✓