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Timeline for The letters of the word "ART"

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Dec 22, 2014 at 9:45 comment added Joonas Ilmavirta @AliTaghavi, you are right. Local compactness seems to fail at the boundary of the accumulation set $S$.
Dec 22, 2014 at 4:42 comment added Ali Taghavi I think the examples of Will Sawin are not locally compact.
Dec 21, 2014 at 17:23 comment added Joonas Ilmavirta @AliTaghavi, you're most welcome. I did enjoy constructing that example space. My guess is that a Hausdorff $X$ with your property is locally compact but I haven't given it a proper thought.
Dec 21, 2014 at 11:10 comment added Ali Taghavi A question on haussdorf case: Assume that $X$ is haussdorf and satisfies the condition of my question. Is $X$ necessarilly locally compact?
Dec 19, 2014 at 14:52 history answered Joonas Ilmavirta CC BY-SA 3.0