Talk:Lebesgue's number lemma
Latest comment: 2 months ago by Hbghlyj in topic Subtle error in proof
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"The" Lebesgue number
editWhy is it called "the" Lebesgue number in the article? It's clear from the definition that it's not unique. skeptical scientist (talk) 18:07, 9 October 2008 (UTC)
- Agreed, so I've changed it. Ben (talk) 05:40, 7 December 2008 (UTC)
Subtle error in proof
editIf U is the cover consisting of just the set X itself, then the function f is not well defined since you can't find the distance to an empty set. In this case, the proof is easy though. Perhaps this should be added? -- 14:55, 13 October 2014 2600:1004:b058:6539:a899:26a6:e47c:c976
- Fixed. --Hbghlyj (talk) 22:29, 18 May 2024 (UTC)
Applications
editThe article mentions that the concept of Lebesgue number is "useful in other applications as well". Which other applications? Either an expert should fill in or this should be removed. — Preceding unsigned comment added by 2601:C0:C400:91A9:444D:6BB0:F609:45F5 (talk) 22:29, 17 June 2018 (UTC)
- A variant (extension, modification) of this lemma is the "Courant–Lebesgue lemma", which bounds the size of maps from the complex plane to surfaces with metric. It is used to prove the existence of harmonic maps between Riemann surfaces. See Jost, "Compact Riemann Surfaces" textbook. 67.198.37.16 (talk) 23:30, 2 March 2024 (UTC)