# Is every compact subset of a second countable space closed? [closed]

I know that this is true for Hausdorff spaces and metric spaces, which are Hausdorff spaces, but I can’t prove it for second countable spaces. Is it even true? Thanks!

$$X=\Bbb N$$ in the co-finite topology is $$T_1$$ but not Hausdorff and trivially second countable as there are only countably many open sets, and every subset of it is compact, but only the finite ones and $$X$$ are closed...