Non-archimedean uniform space

Question

I know about uniform spaces and read this question:

A property of uniform spaces

Now I am very curious and I would like to learn more about these non-Archimedean uniform spaces.

For instance, I am wondering if all non-Archimedean uniformities come from systems of non-Archimedean pseudo-metrics. Or am I wrong with this conjecture?

Can anybody give me some references for this topic where the basic observations are written down? Thank you in advance!

Answer 1

In the book Non-Archimedean functional analysis by van Rooij, Arnoud CM, New York: Dekker, 1978, there is a section on Non-archimedean uniform spaces on pages 34-38. In particular, on page 38, provides a list of references that discuss the problem of ultrametrizability of uniform spaces.

Enjoy!