Countably Compact Metric Space is Sequentially Compact
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Theorem
Let $M$ be a countably compact metric space.
Then $M$ is sequentially compact.
Proof
This follows directly from the results:
$\blacksquare$
Sources
- 1978: Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (2nd ed.) ... (previous) ... (next): Part $\text I$: Basic Definitions: Section $5$: Metric Spaces