Talk:Intrinsic metric

Rename
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

Midpoints

 * The metric d is intrinsic if it has approximate midpoints

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)
 * 1) Sometimes it also taken as a def of intrinsic metric and what is defined here called length metric space, I can not tell waht is the most standard def right now.
 * 2) The statement above is correct if the space is complete. Tosha 19:40, 10 April 2006 (UTC)

d_l vs. d_I
In section Properties, I changed $$d_l$$ to $$d_I$$ 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)


 * I don't think it's an error; I think it stands for "length". Sniffnoy (talk) 19:29, 10 September 2014 (UTC)


 * $$d_l$$ doesn't occur anywhere before "Properties". $$d_I$$ does, and it's the subject of the article. How would you motivate the introduction of $$d_l$$ in section Properties? -- UKoch (talk) 18:23, 13 September 2014 (UTC)


 * Oh, my mistake. I didn't actually take a good look at the old article.  I had mistakenly assumed that $$d_l$$ was used throughout. Sniffnoy (talk) 18:44, 13 September 2014 (UTC)


 * Then it's settled. Something else just occurred to me: It should be $$d_\text{I}$$ rather than $$d_I$$, since the I ("eye") is not a placeholder for anything. I'll make the changes. -- UKoch (talk) 18:25, 14 September 2014 (UTC)

Surely we can do better than this
The section Definitions contains this passage:

"Here, a path'' from $$x$$ to $$y$$ is a continuous map
 * $$\gamma \colon [0,1] \rightarrow M$$

with $$\gamma(0) = x$$ and $$\gamma(1) = y$$. 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)