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Compact Almost Discrete Hypergroups

Published online by Cambridge University Press:  20 November 2018

Michael Voit
Michael Voit*
Affiliation:
Mathematisches Institut Technische Universität München Arcisstr.21 80333 München, Germany, e-mail: voit@mathematik.tu-muenchen.de
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Abstract

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A compact hypergroup is called almost discrete if it is homeomorphic to the one-point-compactification of a countably infinite discrete set. If the group Up of all p-adic units acts multiplicatively on the p-adic integers, then the associated compact orbit hypergroup has this property. In this paper we start with an exact projective sequence of finite hypergroups and use successive substitution to construct a new surjective projective system of finite hypergroups whose limit is almost discrete. We prove that all compact almost discrete hypergroups appear in this way—up to isomorphism and up to a technical restriction. We also determine the duals of these hypergroups, and we present some examples coming from partitions of compact totally disconnected groups.

Keywords

43A6220N2043A4043A10
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 48 , Issue 1 , 01 February 1996 , pp. 210 - 224
Copyright
Copyright © Canadian Mathematical Society 1997

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