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Metrization Theorem for Uniform Loops with the Invertibility Property

Author

Listed:
  • 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)

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.

Suggested Citation

  • Dagmar Markechová & Peter Vrábel & Beáta Stehlíková, 2017. "Metrization Theorem for Uniform Loops with the Invertibility Property," Mathematics, MDPI, vol. 5(2), pages 1-8, June.
    • Handle: RePEc:gam:jmathe:v:5:y:2017:i:2:p:32-:d:100398
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