Category Archives: Point-set topology

Accumulation without converging subsequence

“Any sequence with an accumulation point also has a subsequence converging to that point” — right? I believed this until yesterday when I stumbled over the following curious, and countable, Hausdorff space. Endow with the following topology: is given the … Continue reading

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T_2 and compactness

Any compact (= Hausdorff) space   is on the brink of being compact and being : (1) If we endow with a topology distinct from such that , then is not compact any more; and (2) if we endow with … Continue reading

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