I came across Alexandrov's theorem which says that if X is a Polish space then so is any Gδ subset of X. The set of irrationals appears to be a ground for suspicion : irrationals form a G-delta set of the reals & yet are not a complete metric space ( all under the usual metric).(adsbygoogle = window.adsbygoogle || []).push({});

There is, of course, a metric under which the irrationals are complete.Could someone clarify this? Thanks.

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# On Alexandrov's theorem

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