- #1

demonelite123

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i have already shown that any space X with the cofinite topology is compact since any open cover has a finite subcover on X. i know that if we are dealing with metric spaces, then the notions of compactness and sequentially compactness are equivalent but in general topological spaces it is not true.

so the cofinite topology defines all the open sets as subsets of X whose complement is finite. and a sequentially compact set is a set which has the property that all sequences in the set have a convergent subsequence in the set.

these are the definitions i have but i am not sure how to use them together to show that the set X is sequentially compact. can someone give me some pointers in the right direction? thanks.