Assignment:
Q1. 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.
Q2.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?
Provide complete and step by step solution for the question and show calculations and use formulas.