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.

Other articles related to "topological property, topological":

Topological Property - Common Topological Properties - Miscellaneous
... All topological groups are homogeneous ... These are precisely the finitely generated members of the category of topological spaces and continuous maps ...

Famous quotes containing the word property:

    Those whom the gods chose as their property must not consort with mortals.
    Franz Grillparzer (1791–1872)