topological group (obsolete)

This entry is obsolete, having been superseded by a new entry ( It is being retained for a short while because of the attached thread.

A topological groupMathworldPlanetmath is a triple (G,,𝒯) where (G,) is a group and 𝒯 is a topologyMathworldPlanetmath on G such that under 𝒯, the group operationMathworldPlanetmath (x,y)xy is continuous with respect to the product topology on G×G and the inverse map xx-1 is continuous on G.

Many authors require that the topology be HausdorffPlanetmathPlanetmath.

Title topological group (obsolete)
Canonical name TopologicalGroupobsolete
Date of creation 2013-03-22 12:12:54
Last modified on 2013-03-22 12:12:54
Owner rspuzio (6075)
Last modified by rspuzio (6075)
Numerical id 10
Author rspuzio (6075)
Entry type Definition
Classification msc 22A05
Related topic Group
Related topic TopologicalRing
Related topic BirkhoffKakutaniTheorem
Related topic CategoryOfPolishGroups
Related topic AlgebraicTopology