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Old 2011-03-04, 13:55   #1
hallstei
 
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Default Pseudometric spaces and Lipschitz continuity

Hi,

does anyone know if the concept of Lipschitz continuity is well-defined on pseudometric spaces, the way it is on metric spaces?
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Old 2011-03-04, 15:16   #2
rajula
 
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It is well-defined.
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Old 2011-03-04, 20:43   #3
R.D. Silverman
 
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Quote:
Originally Posted by hallstei View Post
Hi,

does anyone know if the concept of Lipschitz continuity is well-defined on pseudometric spaces, the way it is on metric spaces?
You've asked a question that I can't answer because I do not know
what a pseudometric space is.

Please enlighten me.
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Old 2011-03-05, 01:56   #4
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Quote:
Originally Posted by R.D. Silverman View Post
You've asked a question that I can't answer because I do not know
what a pseudometric space is.

Please enlighten me.
Never mind. I looked it up. I have never encountered a metric space
where d(x,y) can equal 0 for some x!=y. Does anyone have a natural
example where the space is defined on a Riemann manifold? What might
such a distance function look like?

Can a (topological) subspace of (say) a Banach or Hilbert space be
pseudometric?

As I have said before, topology is one of my weak areas.
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Old 2011-03-05, 09:54   #5
hallstei
 
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Quote:
Originally Posted by rajula View Post
It is well-defined.
Thank you very much.
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