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Topological property
(Redirected from Topological invariant)
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 proof 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 set
- 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
Last updated: 10-18-2005 01:30:35
03-10-2013 05:06:04
The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details
The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details