Metrization Theorem for Uniform Loops with the Invertibility Property

Dagmar Markechová, Peter Vrábel and Beáta Stehlíková
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Dagmar Markechová: Department of Mathematics, Faculty of Natural Sciences, Constantine the Philosopher University in Nitra, A. Hlinku 1, SK-949 74 Nitra, Slovakia
Peter Vrábel: Department of Mathematics, Faculty of Natural Sciences, Constantine the Philosopher University in Nitra, A. Hlinku 1, SK-949 74 Nitra, Slovakia
Beáta Stehlíková: Department of Informatics and Mathematics, Faculty of Economy and Business, Pan European University, SK-851 05 Bratislava, Slovakia

Mathematics, 2017, vol. 5, issue 2, 1-8

Abstract: In this paper, we have proved a metrization theorem that gives the sufficient conditions for a uniform IP-loop X to be metrizable by a left-invariant metric. It is shown that by consideration of topological IP-loop dual to X we obtain an analogical theorem for the case of the right-invariant metric.

Keywords: quasigroup; topological IP-loop; left-invariant uniformity; invariant metrics (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2017
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