Existence of Weakly Locally Compact Space which is not Strongly Locally Compact/Proof 2
Jump to navigation
Jump to search
Theorem
There exists at least one example of a weakly locally compact topological space which is not also a strongly locally compact space.
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.
$\blacksquare$