Continuous Functions on Zp

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


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.


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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