4
$\begingroup$

Let $X$ be a set, and $\mathcal{C}$ be a set of subsets of $X$ which contains the empty set and is closed under finite unions and infinite intersections.

Is it true that there must exist a topology on $X$ such that the compact sets of $X$ are $\mathcal{C}$? If not, what other properties does $\mathcal{C}$ need to satisfy for this to be true?

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.