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facenian

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- Problem with a limit point compact space

Hello, I have a problem with a question in Munkres topology book. Munkres asks if a limit point compact subspace X in a Hausdorff space Z is closed.

I tried to prove it by contradiction by taking an infinite set in X and suppose it has a limit point that is not in X, however, I could not find a contradiction. I suspect that an example exists where X is not closed. Can somebody please help?

I tried to prove it by contradiction by taking an infinite set in X and suppose it has a limit point that is not in X, however, I could not find a contradiction. I suspect that an example exists where X is not closed. Can somebody please help?