Talk:Metric Space Compact iff Complete and Totally Bounded

This proof shows that a complete and totally bounded space is sequentially compact, not compact. The result is true, but we're missing the part that shows compactness and sequential compactness are equivalent in metric spaces. I'm currently trying to fill that gap.--Cañizo 20:30, 23 February 2009 (UTC)

Anybody mind if we rename this page to something more descriptive? --Matt Westwood 20:09, 25 February 2009 (UTC)

Done. We might want to delete that old redirect, [[Compactness, Completeness and Boundedness]], but I'll leave that up to you guys. --Cynic (talk) 21:47, 25 February 2009 (UTC)

Done. --Matt Westwood 21:53, 25 February 2009 (UTC)

BTW I'll get round to defining "complete" before too long ... --Matt Westwood 21:54, 25 February 2009 (UTC)

According to my notes this result is (at least sometimes) known as the Hausdorff criterion, although that does have the disadvantage of sounding like a criterion for Hausdorffness --Linus44 06:34, 18 February 2011 (CST) (signed!)