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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

Apr 22

new question: Prove that for any sets A, B, and C, An(BUC)=(AnB)U(AnC) by St_Louis

Apr 20

new image: information-theoretic-distributed-measurement-dds.png by rspuzio

new image: information-theoretic-distributed-measurement-4.2 by rspuzio

new image: information-theoretic-distributed-measurement-4.1 by rspuzio

new image: information-theoretic-distributed-measurement-3.2 by rspuzio

new image: information-theoretic-distributed-measurement-3.1 by rspuzio

new image: information-theoretic-distributed-measurement-2.1 by rspuzio

Apr 19

new collection: On the Information-Theoretic Structure of Distributed Measurements by rspuzio

Apr 15

new question: Prove a formula is part of the Gentzen System by LadyAnne

Mar 30

new question: A problem about Euler's totient function by mbhatia

new question: Prove that for any sets A, B, and C, An(BUC)=(AnB)U(AnC) by St_Louis

Apr 20

new image: information-theoretic-distributed-measurement-dds.png by rspuzio

new image: information-theoretic-distributed-measurement-4.2 by rspuzio

new image: information-theoretic-distributed-measurement-4.1 by rspuzio

new image: information-theoretic-distributed-measurement-3.2 by rspuzio

new image: information-theoretic-distributed-measurement-3.1 by rspuzio

new image: information-theoretic-distributed-measurement-2.1 by rspuzio

Apr 19

new collection: On the Information-Theoretic Structure of Distributed Measurements by rspuzio

Apr 15

new question: Prove a formula is part of the Gentzen System by LadyAnne

Mar 30

new question: A problem about Euler's totient function by mbhatia

## 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 ✓