Definition talk:Quasimetric

Overlap

The way these are defined (at least here), we theoretically should also have a Pseudoquasimetric to accomplish both weakenings of metric simultaneously. --Dfeuer (talk) 17:35, 11 January 2013 (UTC)

Theoretically. I'd rather wait until someone finds a worthwhile result about such notions. --Lord_Farin (talk) 17:40, 11 January 2013 (UTC)

I don't know anything about quasimetrics, but I imagine that for a lot of concepts we would have to have "If blah is a pseudometric or quasimetric then blah blah" in a lot of definitions and probably some theorems. As it is, I've been using "metric or pseudometric"--though there's no mathematical reason to do so, it should help limit confusion among students who haven't encountered pseudometric spaces. --Dfeuer (talk) 17:50, 11 January 2013 (UTC)

A similar construct is applied to some pages, where we write "field or division ring". --Lord_Farin (talk) 17:54, 11 January 2013 (UTC)

Right: the only trouble is that with quasimetrics too, we end up with a list of three. --Dfeuer (talk) 18:02, 11 January 2013 (UTC)

Then leave it out. They're not really covered at this moment anyway. When the need arises, we'll reconsider. --Lord_Farin (talk) 18:18, 11 January 2013 (UTC)

As pseudometrics and quasimetrics have limited visibility in the mathematical world compared to metrics, I would recommend that we just don't bother to mention the applicability of the various theorems to anything by metrics. If you have a direction to go with it, then that's as maybe.

And rather than provide a complicated sentence at the top of each page saying "if blah is a metric space or quasimetric space or etc. puke" we provide a page proving the theorem for a metric only. Then if you want to expand it to a qm or pm you write another page and prove what you got to prove separately. Because nine times out of ten you'll have a separate proof to write anyway. --prime mover (talk) 18:19, 11 January 2013 (UTC)

That's the thing, Prime.mover: nine times out of ten the proofs are identical because the "distinct points have non-zero distance" condition isn't used. --Dfeuer (talk) 18:21, 11 January 2013 (UTC)

I'm speaking of pseudometrics. I don't know jack about quasimetrics. --Dfeuer (talk) 18:22, 11 January 2013 (UTC)

That's as maybe, but my point still stands. --prime mover (talk) 18:28, 11 January 2013 (UTC)

I thought this site was all about breaking things down as much as possible. Copying an entire proof to change one word that doesn't actually relate to the proof in any way is the opposite of that. --Dfeuer (talk) 18:39, 11 January 2013 (UTC)

No, we wouldn't do it like that. --prime mover (talk) 19:06, 11 January 2013 (UTC)