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)