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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Hypergroups with invariant metric


Author: Michael Voit
Journal: Proc. Amer. Math. Soc. 126 (1998), 2635-2640
MSC (1991): Primary 43A62; Secondary 20N20, 54E35
MathSciNet review: 1451835
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Abstract: The purpose of this note is to extend the following classical result from groups to hypergroups in the sense of C.F. Dunkl, R.I. Jewett, and R. Spector: If a hypergroup has a countable neighborhood base of its identity, then $K$ admits a left- or a right-invariant metric. Moreover, it admits an invariant metric if and only if there exists a countable conjugation-invariant neighborhood base of the identity.


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Additional Information

Michael Voit
Affiliation: Mathematisches Institut, Universität Tübingen, 72076 Tübingen, Germany; Department of Mathematics, University of Virginia, Kerchof Hall, Charlottesville, Virginia 22903-3199
Email: voit@uni-tuebingen.de

DOI: http://dx.doi.org/10.1090/S0002-9939-98-04366-4
PII: S 0002-9939(98)04366-4
Keywords: Hypergroups, invariant metric
Received by editor(s): December 26, 1996
Received by editor(s) in revised form: January 27, 1997
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1998 American Mathematical Society