topological invariant

A topological invariantPlanetmathPlanetmath of a space X is a property that depends only on the topologyMathworldPlanetmathPlanetmath of the space, i.e. it is shared by any topological space homeomorphic to X. Common examples include compactness (, connectedness (, Hausdorffness (, Euler characteristicMathworldPlanetmath, orientability (, dimensionMathworldPlanetmath (, and like homology, homotopy groupsMathworldPlanetmath, and K-theory.

Properties of a space depending on an extra structureMathworldPlanetmath such as a metric (i.e. volume, curvature, symplectic invariants) typically are not topological invariants, though sometimes there are useful interpretationsMathworldPlanetmath of topological invariants which seem to depend on extra information like a metric (for example, the Gauss-Bonnet theorem).

Title topological invariant
Canonical name TopologicalInvariant
Date of creation 2013-03-22 13:42:07
Last modified on 2013-03-22 13:42:07
Owner bwebste (988)
Last modified by bwebste (988)
Numerical id 5
Author bwebste (988)
Entry type Definition
Classification msc 54-00