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 $\struct {G, \tau}$ is Hausdorff and:


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