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.

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