mersenneforum.org Pseudometric spaces and Lipschitz continuity
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 2011-03-04, 13:55 #1 hallstei     Apr 2005 158 Posts 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?
 2011-03-04, 15:16 #2 rajula     "Tapio Rajala" Feb 2010 Finland 13B16 Posts It is well-defined.
2011-03-04, 20:43   #3
R.D. Silverman

"Bob Silverman"
Nov 2003
North of Boston

22×1,877 Posts

Quote:
 Originally Posted by hallstei 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.

2011-03-05, 01:56   #4
R.D. Silverman

"Bob Silverman"
Nov 2003
North of Boston

22×1,877 Posts

Quote:
 Originally Posted by R.D. Silverman 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.

2011-03-05, 09:54   #5
hallstei

Apr 2005

D16 Posts

Quote:
 Originally Posted by rajula It is well-defined.
Thank you very much.

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