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!

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Sequence of closed sets

**Physics Forums | Science Articles, Homework Help, Discussion**