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I think this article should be moved to "Length space" or "Length metric". Also, there should be a definition of "Geodesic length space". I'll make these changes in a few weeks if no-one comments further. WLior -- 2006-3-25
The statement is false, as is shown by the rationals. It's possibly true if the space is path-connected, but I'm a little wary: what if none of the paths connecting x and y is rectifiable? AxelBoldt 06:20, 10 April 2006 (UTC)
In section Properties, I changed to throughout. It's hard to see the difference with a sans serif font, and d_l ("ell") makes no sense to me, so I think the ell must have been an error. -- UKoch ( talk) 19:41, 9 September 2014 (UTC)
The section Definitions contains this passage:
"Here, a path from to is a continuous map
with and . The length of such a path is defined as explained for rectifiable curves."
Oh, come on. Instead of referring the reader to the entire article on rectifiable curves — which contains many definitions of length of a path that are not appropriate for continuous curves — this article should just give the appropriate definition for continuous curves. 216.161.117.162 ( talk) 20:18, 25 August 2020 (UTC)
![]() | This article is rated Start-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | ||||||||||
|
I think this article should be moved to "Length space" or "Length metric". Also, there should be a definition of "Geodesic length space". I'll make these changes in a few weeks if no-one comments further. WLior -- 2006-3-25
The statement is false, as is shown by the rationals. It's possibly true if the space is path-connected, but I'm a little wary: what if none of the paths connecting x and y is rectifiable? AxelBoldt 06:20, 10 April 2006 (UTC)
In section Properties, I changed to throughout. It's hard to see the difference with a sans serif font, and d_l ("ell") makes no sense to me, so I think the ell must have been an error. -- UKoch ( talk) 19:41, 9 September 2014 (UTC)
The section Definitions contains this passage:
"Here, a path from to is a continuous map
with and . The length of such a path is defined as explained for rectifiable curves."
Oh, come on. Instead of referring the reader to the entire article on rectifiable curves — which contains many definitions of length of a path that are not appropriate for continuous curves — this article should just give the appropriate definition for continuous curves. 216.161.117.162 ( talk) 20:18, 25 August 2020 (UTC)