1. The problem statement, all variables and given/known data E is a compact set, F is a closed set. Prove that intersection of E and F is compact 2. Relevant equations 3. The attempt at a solution On Hausdoff space (the most general space I can work this out), compact set is closed. So E is closed. So intersection of E and F is closed. That is a closed subset of compact set E so intersection of E and F is closed. My problem is i can't generalize the proof to general topological space. If E is not in Hausdoff space, it is not necessarily closed. I don't know if I was going in the right direction or not. Please help me with it. Thank you very much.