Countably Compact First-Countable Space is Sequentially Compact/Proof 1
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Theorem
A countably compact first-countable topological space is also sequentially compact.
Proof
Follows directly from:
- Infinite Sequence in Countably Compact Space has Accumulation Point
- Accumulation Point of Infinite Sequence in First-Countable Space is Subsequential Limit
$\blacksquare$