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Nov 17, 2022 at 9:43 comment added Lucas L. Ah, that's exactly what I needed. Thank you very much!
Nov 17, 2022 at 9:42 vote accept Lucas L.
Nov 16, 2022 at 14:52 comment added Anton Petrunin @LucasL. The intersection is isometric to a subsets in $\mathbb{R}\times C(\mathbb{S}^1_\alpha)$ as well as in $C(\Sigma_p)$. In particular, $C(\Sigma_p)$ contains a subset isometric to a neighborhood of a singular point in $\mathbb{R}\times C(\mathbb{S}^1_\alpha)$.
Nov 16, 2022 at 13:25 comment added Lucas L. Hi Anton, thanks for the answer! Yes, my mistake, I should’ve excluded the endpoints of course. Either way, if U and B intersect, what happens to the metric at the intersection? There should be some compatibility, no? Thanks again.
Nov 15, 2022 at 21:20 history answered Anton Petrunin CC BY-SA 4.0