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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.
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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
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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.
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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. --
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of a path that are not appropriate for continuous curves — this article should just give the appropriate definition for continuous curves.
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Oh, come on. Instead of referring the reader to the entire article on rectifiable curves — which contains
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Oh, my mistake. I didn't actually take a good look at the old article. I had mistakenly assumed that
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on
Knowledge. If you would like to participate, please visit the project page, where you can join
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does, and it's the subject of the article. How would you motivate the introduction of
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Then it's settled. Something else just occurred to me: It should be
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I don't think it's an error; I think it stands for "length".
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The statement above is correct if the space is complete.
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The metric d is intrinsic if it has approximate midpoints
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