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)