Talk:First-Countable Space is Sequentially Compact iff Countably Compact

In light of what's going on in Sequences_in_a_Compact_Space_Have_a_Convergent_Subsequence, some of the wording in this page probably needs a small change.

-- Qedetc 17:02, 12 June 2011 (CDT)


 * Should it? Probably not. This page talks about countable compactness and doesn't go near compactness.


 * Although we could always put a second proof up saying: since compactness implies countable compactness then we can use blah blah ... etc. --prime mover 17:19, 12 June 2011 (CDT)

Whoops, no. I'm crazy and misread the line
 * We have that a Sequentially Compact Space is Countably Compact whether the space is first-countable or not.

I forget how I got to this page now even. I think I followed a "what links here" trail and had the other thing on my mind since I was working on it. Sorry :P

-- Qedetc 18:27, 12 June 2011 (CDT)