Pseudometric spaces and Lipschitz continuity

[hallstei]

Hi,

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

[rajula]

It is well-defined.

[R.D. Silverman]

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.

Please enlighten me.

[R.D. Silverman]

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.

[hallstei]

Originally Posted by rajula

It is well-defined.

Thank you very much.