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Nov 20, 2009 at 15:32 comment added Greg Kuperberg This Wikipedia page is an excellent answer to the question. Urysohn's theorem (second-countable, regular, Hausdorff is metrizable) and Smirnov's theorem (locally metrizable, Hausdorff, paracompact is metrizable) really are what people use all the time.
Nov 20, 2009 at 15:23 history answered user709 CC BY-SA 2.5