suggest study material for p-adic metric and ultra metric etc.

Question

Well,in the book , Elementary Topology Problem Textbook I first found some problems defining p-adic and ultra metric. They have a few problems on it. Now I thought of reading those two types in details but could not find much in any book or on the net except 4-5 properties of ultra metric on WikiPedia.I figured since these are not exactly metric spaces , their properties should be somewhat different from metric spaces.

So, are there any study materials/books that have some chapter dedicated to these ?Where can I study them further?

Answer 1

Stephen Semmes has some good material on these kinds of things on the arXiv: see, for example

• https://arxiv.org/abs/0711.0709 (An introduction to the geometry of ultrametric spaces)
• https://arxiv.org/abs/1306.2421 (Some basic aspects of analysis on metric and ultrametric spaces)