Category:Definitions/Locally Compact Topological Groups
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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.
Pages in category "Definitions/Locally Compact Topological Groups"
The following 5 pages are in this category, out of 5 total.