topological group (obsolete)

This entry is obsolete, having been superseded by a new entry (http://planetmath.org/TopologicalGroup2). It is being retained for a short while because of the attached thread.

A topological group is a triple $(G,\cdot ,𝒯)$ where $(G,\cdot )$ is a group and $𝒯$ is a topology on $G$ such that under $𝒯$, the group operation $(x,y)\mapsto x\cdot y$ is continuous with respect to the product topology on $G\times G$ and the inverse map $x\mapsto x^{-1}$ is continuous on $G$.

Many authors require that the topology be Hausdorff.

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