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?

It is well-defined.

[QUOTE=hallstei;254289]Hi,

does anyone know if the concept of Lipschitz continuity is well-defined on pseudometric spaces, the way it is on metric spaces?[/QUOTE]

You've asked a question that I can't answer because I do not know
what a pseudometric space is.

Please enlighten me.

[QUOTE=R.D. Silverman;254325]You've asked a question that I can't answer because I do not know
what a pseudometric space is.

Please enlighten me.[/QUOTE]

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.

[QUOTE=rajula;254295]It is well-defined.[/QUOTE]

Thank you very much.