Sequentially Compact Metric Space is Separable and Second-Countable
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(Redirected from Sequentially Compact Metric Spaces are Separable and Second-Countable)
Theorem
A sequentially compact metric space is separable and second-countable.
Proof
A sequentially compact metric space is totally bounded, and a totally bounded space is separable and second-countable.
$\blacksquare$
