\begin{definition}[Definition:Locally Compact Hausdorff Space/Definition 2]
Let $T = \left({S, \tau}\right)$ be a Hausdorff topological space.
$T$ is a '''locally compact Hausdorff space''' {{iff}} each point has a neighborhood basis consisting of compact sets.
That is, {{iff}} $T$ is locally compact (in the general sense).
Category:Definitions/Compact Spaces
\end{definition}