I was reading about the Nested sphere theorem and a thought occurred. if you have a sequence of decreasing closed sets whose diameter goes to zero in the limit,(adsbygoogle = window.adsbygoogle || []).push({});

we can show that the intersection of all these sets is a single point.

my idea was to show this using nested sphere theorem if we can say that for any closed set we can find a smallest closed sphere containing this set as well as a biggest sphere contained in this set.

that way we can trap our original sequence between two sequences of decreasing spheres.

Is this if fact possible? if so/not, why?

cheers!

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# Sequence of closed sets

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