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Projective and Inductive Limits of Hypergroups
Author(s) -
Voit Michael
Publication year - 1993
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/s3-67.3.617
Subject(s) - mathematics , coset , projective test , duality (order theory) , pure mathematics , commutative property , dual (grammatical number) , discrete mathematics , algebra over a field , linguistics , philosophy
The purpose of this paper is to introduce projective and inductive limits of hypergroups and to discuss their basic properties in a systematic way. In particular, we study the behaviour of these limits with a view to forming coset and double coset hypergroups, and determine the dual spaces of these limits. As a consequence, some duality results for certain commutative hypergroups can be extended to wider classes. Our results will be illustrated by hypergroups associated with Gelfand pairs for which some of the results are well known.