Does there exist a topology which can be induced simultaneously by a complete and an incomplete uniformity?
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1$\begingroup$ Related: Two metrics induce the same topology, but one is complete and the other isn't $\endgroup$– Martin SleziakCommented Oct 1, 2017 at 13:01
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$\begingroup$ @MartinSleziak Can you tell me any book that discusses it. $\endgroup$– JaveCommented Oct 1, 2017 at 16:21
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$]0,1[$ and the real line are, famously, homeomorphic but the latter is complete whereas the former is not (both under the usual metric).
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$\begingroup$ Can you tell me any book that discusses it $\endgroup$– JaveCommented Oct 2, 2017 at 18:27