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 given two topological spaces X and Y and a homeomorphism f between them, a topological property for a subset A of X holds if and only if it holds for f(A).
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.
Topological properties
- open and closed sets (an automorphism on a topological space preserves open and closed sets)
- interior and closure
- neighbourhood
- limit point
- compactness
- connectedness
- Hausdorff
- the winding number used in complex analysis
- nowhere dense set, set of first category or meager set, set of second category
- separability
- metrizability and uniformizability