There is a theorem: If {En} is a sequence of(adsbygoogle = window.adsbygoogle || []).push({}); closed,nonemptyandboundedsets in acompletemetric space X, if En[tex]\supset[/tex]En+1, and if lim diam En = 0, then [tex]\cap[/tex]En consists exactly one point.

And what I'm asking is that, if either the sets were not closed or X was not a complete space (but not both), and all other condictions are still satisfied, then what will follow? And if I let X be the rational set, for instance, what will I get. And could you explain it?

Thks.

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# A question to Sequence.

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