Talk:Sequentially Compact Metric Space is Compact/Proof 3

I'm not sure this does the job.

You have Sequentially Compact Metric Space is Separable and Second-Countable.

But from Second-Countable Space is Compact iff Countably Compact, all you have is that if a second countable space is countably compact, then it is compact (and vice versa). It still needs to be proved that a sequentially compact metric space is actually countably compact. --prime mover (talk) 20:54, 31 October 2012 (UTC)


 * Yeah, I messed up. It should be fixed now. --abcxyz (talk) 21:11, 31 October 2012 (UTC)