A topological space X is KC – space if every compact subsets are closed.
question:
Does a KC - space contains a minimal KC topology?
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1See http://mathoverflow.net/questions/137660/katetov-kc-and-sequental-spaces. – user87690 Jul 27 '13 at 18:47
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The answer is no; Bill Fleissner constructed a counterexample in ‘A $T_B$ space which is not Katetov $T_B$’, which is freely available here. (He uses the term $T_B$ space for your KC-space.)
Brian M. Scott
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