# A compact subset $Y$ of a topological space $X$ is not necessarily closed. [duplicate]

Possible Duplicate:
Compact sets are closed?

We know that if $X$ is Hausdorff, then a compact subset $Y$ of $X$ must be closed. Without the assumption, this claim is not true. But can you come up with a counterexample?

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## marked as duplicate by Austin Mohr, amWhy, Potato, Alexander Gruber♦, Asaf KaragilaJan 5 '13 at 9:48

Do you know any non-Hausdorff spaces? – Zev Chonoles Jan 5 '13 at 3:30

Give any set with at least two elements the indiscrete topology. Then any nonempty proper subset is compact but not closed.

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