Category:Definitions/Locally Compact Topological Groups

This category contains definitions related to Locally Compact Topological Groups.
Related results can be found in Category:Locally Compact Topological Groups.

Let $\struct {G, \odot, \tau}$ be a topological group.

Definition 1

We say that $\struct {G, \odot, \tau}$ is a locally compact topological group if and only if $\struct {G, \tau}$ is a locally compact Hausdorff space.

Definition 2

Let $e$ be the identity element of $\struct {G, \odot}$.

We say that $\struct {G, \odot, \tau}$ is a locally compact topological group if and only if $\struct {G, \tau}$ is Hausdorff and:

there exists an open neighborhood $U$ of $e$ such that the topological closure of $U$ in $\struct {G, \tau}$ is compact.