Greetings, I'm helping out a student with her upcoming topology exam and something has be stomped. It's probably simple but I'm not seeing it at the moment. Consider a Hausdorf space (X,T). Any compact subset of X is therefore closed. The question is to prove the existence of a coarser topology on (X,T) so that closed also implies compactness. I'm basically trying to find a coarser topology on X that makes it compact. Thanks in advance.