topological invariant
A topological invariant of a space is a property that depends only on the topology
of the space, i.e. it is shared by any topological space homeomorphic to . Common examples include compactness (http://planetmath.org/Compact
), connectedness (http://planetmath.org/ConnectedSpace), Hausdorffness (http://planetmath.org/T2Space), Euler characteristic
, orientability (http://planetmath.org/Orientation2), dimension
(http://planetmath.org/InvarianceOfDimension), and like homology, homotopy groups
, and K-theory.
Properties of a space depending on an extra structure such as a metric (i.e. volume, curvature, symplectic invariants) typically are not topological invariants, though sometimes there are useful interpretations
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 |