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 (x ∈ Q 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.
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© 2000 Springer Science+Business Media New York
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Robert, A.M. (2000). Continuous Functions on Z p . In: A Course in p-adic Analysis. Graduate Texts in Mathematics, vol 198. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-3254-2_4
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DOI: https://doi.org/10.1007/978-1-4757-3254-2_4
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-3150-4
Online ISBN: 978-1-4757-3254-2
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