Is every countably compact subset of a Hausdorff space closed? It is known that a compact subset of a Hausdorff space is closed. So, I have a question: Is every countably compact subset of a Hausdorff space closed?

The subspace $\Sigma = \{f \in [0,1]^\mathbb{R}: \left|\{x: f(x) \neq 0\}\right| \le \aleph_0 \}$ of the compact space $[0,1]^\mathbb{R}$ is countably and sequentially compact but not closed.
