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.

Contents

Common topological properties

Cardinal functions

Separation

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

Connectedness

Compactness

Metrizability

Miscellaneous

See also

References