Compact Space is Weakly Sigma-Locally Compact
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Theorem
Let $T = \struct {S, \tau}$ be a compact space.
Then $T$ is a weakly $\sigma$-locally compact space.
Proof
Let $T = \struct {S, \tau}$ be a compact space.
We have that:
Hence by definition $T$ is weakly $\sigma$-locally compact space.
$\blacksquare$
Sources
- 1978: Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (2nd ed.) ... (previous) ... (next): Part $\text I$: Basic Definitions: Section $3$: Compactness: Localized Compactness Properties