3) Let X have the following property: for any x and y in X such that x #y there exists disjoint open sets U and V such that x = U and y = V. Let F be a compact subset of X and let x F. Prove that there are disjoint open sets U and V such that E x = U and FC V. Use Heine Borel version of compactness: every open cover of F admits a finite subcover.