\begin{definition}[Definition:Locally Compact Hausdorff Space/Definition 1]
Let $T = \left({S, \tau}\right)$ be a Hausdorff topological space.
$T$ is a '''locally compact Hausdorff space''' {{iff}} each point of $S$ has a compact neighborhood.
That is, {{iff}} $T$ is weakly locally compact.
Category:Definitions/Compact Spaces
\end{definition}