Talk:Locally simply connected space
Latest comment: 3 months ago by TakuyaMurata in topic This page cites a definition to Hatcher which does not appear there
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This page cites a definition to Hatcher which does not appear there
editThe current definition is cited to Hatcher, but does not appear in the linked version of that book.
The current definition does not appear in that exact form in Munkres' book either.
The definition of locally simply connected to be considered standard seems to be a somewhat contentious topic, and this page does not make this clear. I.e., see the following link: https://mathoverflow.net/questions/487326/definition-of-locally-simply-connected-space
Borsuk's definition seems to be the original one. Also see this page: https://math.stackexchange.com/questions/1082601/anr-is-locally-contractible/3926424#3926424 ~2026-89400-7 (talk) 18:11, 26 February 2026 (UTC)
- Yes, they are not good references for precise definitions (they are good as textbooks though). I have commented out the references for now. Basically the problem is that “locally” is somehow ambiguous in topology; *usually* locally X means there is a neighborhood basis consisting of those with X so I think the definition we are giving is correct (just need a confirmation) —- Taku (talk) 02:16, 13 March 2026 (UTC)