Continuous Functions on Zp

  • Alain M. Robert
Part of the Graduate Texts in Mathematics book series (GTM, volume 198)

Abstract

The goal of this chapter is the study of continuous functions on subsets of the p-adic field Q p with values in an extension of Q p. Since Q p admits a partition into clopen balls x + Z p (xQ p /Z p = Z[1/p]/Z), it is enough to study continuous functions on Z p. Thus, we shall typically study continuous functions Z p C p . Since the natural numbers N form a dense subset of the ring Z p , we shall start by the study of functions on N or Z and with values in any abelian group.

Keywords

Assure Convolution 

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Copyright information

© Springer Science+Business Media New York 2000

Authors and Affiliations

  • Alain M. Robert
    • 1
  1. 1.Institut de MathématiquesUniversité de NeuchâtelNeuchâtelSwitzerland

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