On the arithmetical structure of some compact subsets in the \(p-\)adic complex number field

Angel Popescu
Department of Mathematics, Technical University of Civil Engineering of Bucharest, Romania.

\(^{1}\)Corresponding Author: popescuangel@yahoo.co.uk

Copyright © 2005 Angel Popescu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Published: December, 2005

Abstract

We use arithmetical tools (algebraic numbers, valuations, Galois groups) in order to describe the structure of all compact subsets of the \(p-\)adic complex field, which are invariant with respect to the absolute Galois group of the \(p-\)adic number field

Keywords:

Galois groups, number fields, Banach algebras, compact sets.