Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 43A62, 20N20, 54E35

Retrieve articles in all journals with MSC (1991): 43A62, 20N20, 54E35

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

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