Intersection of collection of open intervals

Reference no: EM13134661

1. Prove if F is a subset of R^n and if d(x,F)=inf(||x-z||:z in F}=0 then x belongs to F.

2. The intersection of two open sets is compact iff it is empty. Can the intersection of an infinite collection of open sets be a non-empty compact set?

Reference no: EM13134661

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