Excluded Point Space is Sequentially Compact
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Theorem
Let $T = \struct {S, \tau_{\bar p} }$ be an excluded point space.
Then $T$ is a sequentially compact space.
Proof
- Excluded Point Space is Compact
- Compact Space is Countably Compact
- Excluded Point Space is First-Countable
$\blacksquare$
Sources
- 1978: Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (2nd ed.) ... (previous) ... (next): Part $\text {II}$: Counterexamples: $13 \text { - } 15$. Excluded Point Topology: $6$