Let (X,d) be a metric space and A, B non-empty subsets of X. The distance from A to B is defined as dist(A,B)=inf{d(x,y) : x in A, y in B}. a) Let A, B non-empty subsets of X. Prove that if A is compact and B is closed, then dist(A,B)>0
b) Is the previous statement true if B is open instead of closed? (argue your answer)
c) Is it true in general that the distance between two unrelated closed objects is positive? (argue your answer)