Geodesic
Compact Almost Discrete Hypergroups
Canadian journal of mathematics, Tome 48 (1996) no. 1, pp. 210-224

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.4153/CJM-1996-010-8
Mots-clés : 43A62, 20N20, 43A40, 43A10 
Voit, Michael. Compact Almost Discrete Hypergroups. Canadian journal of mathematics, Tome 48 (1996) no. 1, pp. 210-224. doi: 10.4153/CJM-1996-010-8
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