p-Adic Numbers and Adeles

Abstract

The majority of the examples of topological groups in this book given so far, are locally euclidean, meaning that the groups are locally homeomorphic to ${\mathbb R}^n.$ In this chapter the reader will see some examples which are not of this type. These examples, the p-adic numbers and the adeles, resp. ideles, are not only interesting as examples of this theory, but they also carry great importance for other areas of mathematics, in particular number theory.