most recent 30 from http://mathoverflow.net 2013-05-22T20:30:11Z http://mathoverflow.net/feeds/question/6274 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/6274/when-is-a-hausdorff-space-metrisable Aston Smythe 2009-11-20T15:05:17Z 2009-11-20T18:14:41Z

<p>This question may be a little too easy for this site, but I'll ask it anyway: when is a Hausdorff topological space metrisable?</p>

http://mathoverflow.net/questions/6274/when-is-a-hausdorff-space-metrisable/6275#6275 Ho Chung Siu 2009-11-20T15:23:27Z 2009-11-20T15:23:27Z

<p>The wikipedia page <a href="http://en.wikipedia.org/wiki/Metrisability" rel="nofollow">here</a> is probably of interest. It contains links to a few metrization theorems, including results of <a href="http://en.wikipedia.org/wiki/Nagata-Smirnov%5Fmetrization%5Ftheorem" rel="nofollow">Nagata-Smirnov's</a> and <a href="http://en.wikipedia.org/wiki/Bing%5Fmetrization%5Ftheorem" rel="nofollow">Bing's</a>. There is also the Smirnov metrization theorem that appears in Munkres' topology: it states that A space X is metrizable if and only if it is paracompact, Hausdorff, and locally metrizable.</p>

http://mathoverflow.net/questions/6274/when-is-a-hausdorff-space-metrisable/6277#6277 HW 2009-11-20T15:43:51Z 2009-11-20T15:43:51Z

<p>I think it's also worth pointing out the Wikipedia page on <a href="http://en.wikipedia.org/wiki/Moore%5Fspace%5F%28topology%29" rel="nofollow">Moore spaces</a>. It turns out that the <em>full</em> answer to your question (if you don't allow conditions like "locally metrizable") has something to do with the Continuum Hypothesis.</p>