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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Hypergroups with invariant metric
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by Michael Voit PDF
Proc. Amer. Math. Soc. 126 (1998), 2635-2640 Request permission

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
  • MR Author ID: 253279
  • ORCID: 0000-0003-3561-2712
  • Email: voit@uni-tuebingen.de
  • Received by editor(s): December 26, 1996
  • Received by editor(s) in revised form: January 27, 1997
  • Communicated by: Palle E. T. Jorgensen
  • © Copyright 1998 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 126 (1998), 2635-2640
  • MSC (1991): Primary 43A62; Secondary 20N20, 54E35
  • DOI: https://doi.org/10.1090/S0002-9939-98-04366-4
  • MathSciNet review: 1451835