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Mathematics 2017, 5(2), 32; doi:10.3390/math5020032

Metrization Theorem for Uniform Loops with the Invertibility Property

Department of Mathematics, Faculty of Natural Sciences, Constantine the Philosopher University in Nitra, A. Hlinku 1, SK-949 74 Nitra, Slovakia
Department of Informatics and Mathematics, Faculty of Economy and Business, Pan European University, SK-851 05 Bratislava, Slovakia
Author to whom correspondence should be addressed.
Academic Editor: Lokenath Debnath
Received: 2 February 2017 / Revised: 18 May 2017 / Accepted: 30 May 2017 / Published: 2 June 2017
View Full-Text   |   Download PDF [664 KB, uploaded 2 June 2017]


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. View Full-Text
Keywords: quasigroup; topological IP-loop; left-invariant uniformity; invariant metrics quasigroup; topological IP-loop; left-invariant uniformity; invariant metrics
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Markechová, D.; Vrábel, P.; Stehlíková, B. Metrization Theorem for Uniform Loops with the Invertibility Property. Mathematics 2017, 5, 32.

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