Every compact subspace of a Hausdorff space is closed I'm studying the Topology-Munkres book and there is a Theorem that states that Every compact subspace of a Hausdorff space is closed and I was wondering if there is any example where the "Hausdorff" condition is not needed, I mean could you give an example where the statement is fulfill only by Every compact subspace of a space $X$ is closed 
Is just that I'm really bad finding examples and I want to know this, thank you.

If every subspace is closed (like in the discrete topology) then the statement is trivially fulfilled.
