Definition:Locally Compact Topological Group
Jump to navigation
Jump to search
Definition
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.
Also see
Also known as
A locally compact topological group is also known as a locally compact group.