Existence of Weakly Locally Compact Space which is not Strongly Locally Compact/Proof 2

Proof
Let $T$ be an infinite particular point space.

From Particular Point Space is Weakly Locally Compact, $T$ is a weakly locally compact space.

From Infinite Particular Point Space is not Strongly Locally Compact, $T$ is not a strongly locally compact space.

Hence the result.