I Pseudometric Spaces: What Are They and Why Are They Important in Mathematics?

  • I
  • Thread starter Thread starter Paige_Turner
  • Start date Start date
  • Tags Tags
    Space
Paige_Turner
Messages
44
Reaction score
9
TL;DR Summary
What is an example non-Riemannian pseudometric space that is not null or trivial?
I suspect you're not supposed to ask short questions here. Mine is in the summary.
 
Physics news on Phys.org
Various Finsler spaces? (Usually, Finsler metrics are positive definite, but you can have pseudometrics too.)
 
  • Like
Likes wrobel
strangerep said:
Various Finsler spaces?
I never heard of Finsler spaces. Apparently they'e a superset of Riemannian space. But my question involved the latter.
 
What do you understand by non-Riemannian pseudometric space?
 
Paige_Turner said:
I never heard of Finsler spaces. Apparently they'e a superset of Riemannian space. But my question involved the latter.
Umm,... no,... your question involved non-Riemannian spaces.

A Finsler space whose fundamental function (squared) is quadratic in the velocities is Riemannian, but all other Finsler spaces are non-Riemannian.
 
  • Like
Likes robphy
martinbn said:
> What do you understand by non-Riemannian pseudometric space?
I have no idea. It's not my concept. Someone somewhere said that the pseudometric spaces are a proper superset of the Riemannian spaces, but I don't know the difference, and I want to learn what the difference between he two is.

META: Someone asked me not to use the > character to indicate quoted text in replies.

The nonstandard system font I use (apparently) doesn't define whatever characters you use in the editor interface buttons. They look like little rectangles with a unicode hex index inside.

If > isn't okay, how should I indicate quoted text?
 
Last edited:
Paige_Turner said:
If > isn't okay, how should I indicate quoted text?
By using the PF "Reply" feature, which it looks like you are doing okay with. Just don't add an extra character into the quote -- it should be the exact quote from the other person.

When you click-drag a section of another poster's text, then click "Reply", that creates the Quote Box with the other user's username and a little up-arrow that will take folks to the post that the quote came out of.
 
Paige_Turner said:
I have no idea. It's not my concept. Someone somewhere said that the pseudometric spaces are a proper superset of the Riemannian spaces, but I don't know the difference, and I want to learn what the difference between he two is.
Since you're a relatively new PF user, I'll explain that "someone somewhere said" is a good way to get knowlegeable people here to become disinterested in your post.

A likely-more-successful way to get better answers would have been for you to first check what an ordinary Riemannian space is (e.g., on Wikipedia), and what a pseudometric is (also on Wikipedia or other sources available by googling). Similarly, if you google for "pseudo-Riemannian space" you'll get some other references. Then, if anything is still unclear, ask a more specific question here on PF, also mentioning which specific reference sources you have already consulted.
 
  • Like
Likes berkeman, martinbn and robphy
  • #10
I said I didn't remember where I read it.

If I had been talking about F=MA, I wouldn't have to cite that. Similarly, since this simple question is something that real physicists know, i thought that they would recognize it and just respond. If not, it isn't worth making a big deal about.

In any case, one would think you could ask a question here about something as abstract as pseudometric space without being required to say who asked it somewhere else or being told to go look up the answer.
 
  • Skeptical
Likes weirdoguy and berkeman
Back
Top