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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.

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# Question concerning compact subtopologies on Hausdorf spaces

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