Difference between revisions of "Topological property"
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Latest revision as of 14:53, 21 September 2016
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.
Description
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.
See also
- Euler characteristic
- Winding number
- Characteristic class
- Characteristic numbers
- Chern class
- Knot invariant
- Linking number
- Fixed point property
- Topological quantum number
- Homotopy group and Cohomotopy group
- Homology and cohomology
- Quantum invariant
External links
- Topological property @ Wikipedia
