20110304, 13:55  #1 
Apr 2005
1101_{2} Posts 
Pseudometric spaces and Lipschitz continuity
Hi,
does anyone know if the concept of Lipschitz continuity is welldefined on pseudometric spaces, the way it is on metric spaces? 
20110304, 15:16  #2 
"Tapio Rajala"
Feb 2010
Finland
3^{2}×5×7 Posts 
It is welldefined.

20110304, 20:43  #3 
Nov 2003
16373_{8} Posts 

20110305, 01:56  #4  
Nov 2003
3×2,473 Posts 
Quote:
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. 

20110305, 09:54  #5 
Apr 2005
13 Posts 

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