Definition:Locally Compact Topological Group/Definition 2

Definition

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

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.

Sources

• 2014: Loukas Grafakos: Classical Fourier Analysis (3rd ed.) ... (previous) ... (next): $1.1.2$: Examples of Topological Groups