It is well known that every metric space is normal. But how do we know that normal topological spaces are metrizable?
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http://math.stackexchange.com/questions/157906/normal-non-metrizable-spaces – User8976 Mar 27 '17 at 01:29
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2Possible duplicate of Normal, Non-Metrizable Spaces – Ross Millikan Mar 27 '17 at 01:44