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xno163.bsky.social
素晴らしい回答↓
math.stackexchange.com/questions/40...
Hausdorff condition in "continuous image of a compact set is compact"
In the book I'm following, compact spaces are also required to be Hausdorff by definition. Then, is the following oft-cited statement true? Continuous image of a compact space is compact. I guess...
https://math.stackexchange.com/questions/4094546/hausdorff-condition-in-continuous-image-of-a-compact-set-is-compact#:~:text=It%20is%20true%20that%20every%20subspace%20of,spaces%2C%20f:X→Y%20is%20continuous%2C%20X%20is%20quasi%2D
January 11, 2026 at 12:48 PM
xno163.bsky.social
例えば有限集合の離散位相から非離散位相への恒等写像が挙げられます
January 11, 2026 at 12:45 PM
xno163.bsky.social
Hausdorffの連続像はHausdorffとは限らないため

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被覆コンパクトHausdorffの連続像はHausdorffとは限らないため
January 11, 2026 at 12:07 PM