View source for Topological property

In [[topology]] and related areas of [[mathematics]], a '''topological property''' or '''topological invariant''' is a property of a [[topological space]] which is [[Invariant (mathematics)|invariant]] under [[Homeomorphism|homeomorphisms]].

== Description ==

That is, a property of spaces is a topological property if whenever a space X possesses that property every space homeomorphic to X possesses that property.

Informally, a topological property is a property of the space that can be expressed using open sets.

A common problem in topology is to decide whether two topological spaces are homeomorphic or not. To prove that two spaces are not homeomorphic, it is sufficient to find a topological property which is not shared by them.

== See also ==

* [[Euler characteristic]]
* [[Winding number]]
* [[Characteristic class]]
* [[Characteristic numbers]]
* [[Chern class]]
* [[Knot invariant]]
* [[Linking number]]
* [[Fixed point property]]
* [[Topological quantum number]]
* [[Homotopy group and Cohomotopy group]]
* [[Homology]] and [[cohomology]]
* [[Quantum invariant]]

== External links ==

* [https://en.wikipedia.org/wiki/Topological_property Topological property] @ Wikipedia


[[Category:Mathematics]]
[[Category:Topology]]