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 under homeomorphisms. 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.

Common topological properties

Cardinal functions


For a detailed treatment, see separation axiom. Some of these terms are defined differently in older mathematical literature; see history of the separation axioms.

Countability conditions





See also


  1. Juhász, István; Soukup, Lajos; Szentmiklóssy, Zoltán (2008). "Resolvability and monotone normality" (PDF). Israel Journal of Mathematics. The Hebrew University Magnes Press. 166 (1): 1–16. doi:10.1007/s11856-008-1017-y. ISSN 0021-2172. Retrieved 4 December 2012.


This article is issued from Wikipedia - version of the 6/17/2016. The text is available under the Creative Commons Attribution/Share Alike but additional terms may apply for the media files.