Talk:Cantor's intersection theorem

I'm unsure the statement of the theorem as it currently stands is correct, it should either be clear that the spaces in question are metric. Or if the article is intended to deal in more generality it should be more precise as if we take the statement to be about topological spaces it is not correct (we need to assume Haussdorfness). The article did used to make sense when it only dealt with subsets of the reals, but was edited in February and is confusing as stands. Alex J Best (talk) 12:13, 23 May 2013 (UTC)[reply]

My problem with this is that the proof of the Heine–Borel theorem uses Cantor's intersection theorem, and the proof of Cantor's intersection theorem uses the Heine–Borel theorem. Nick Levine (talk) 08:12, 6 August 2013 (UTC)[reply]