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This entry is obsolete, having been superseded by a new entry (http://planetmath.org/TopologicalGroup2).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 $(G,\\cdot,\\mathcal{T})$ where $(G,\\cdot)$ is a group and $\\mathcal{T}$ is a topology on $G$ such that under $\\mathcal{T}$ , 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.

单词	TopologicalGroupobsolete
释义	topological group (obsolete) This entry is obsolete, having been superseded by a new entry (http://planetmath.org/TopologicalGroup2).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 $(G,\\cdot,\\mathcal{T})$ where $(G,\\cdot)$ is a group and $\\mathcal{T}$ is a topology on $G$ such that under $\\mathcal{T}$ , 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.
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