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Topologies of Bihyperbolic Numbers

Author

Listed:
  • Ana Savić

    (School of Electrical and Computer Engineering, Academy of Technical and Art Applied Studies, 11000 Belgrade, Serbia
    These authors contributed equally to this work.)

  • Merve Bilgin

    (Department of Mathematics, Faculty of Sciences, University of Sakarya, 54050 Sakarya, Turkey
    These authors contributed equally to this work.)

  • Soley Ersoy

    (Department of Mathematics, Faculty of Sciences, University of Sakarya, 54050 Sakarya, Turkey
    These authors contributed equally to this work.)

  • Marija Paunović

    (Faculty of Hotel Management and Tourism, University of Kragujevac, 36210 Vrnjacka Banja, Serbia
    These authors contributed equally to this work.)

Abstract

In this paper, we establish a correlation between the bihyperbolic numbers set and the semi-Euclidean space. There are three different norms on the semi-Euclidean space that allow us to define three different hypersurfaces on semi-Euclidean space. Hence, we construct some topological structures on these hypersurfaces called norm e , s , and t topologies. On the other hand, we introduce hyperbolic e , s , and t topologies on the bihyperbolic numbers set. Moreover, by using the idempotent and spectral representations of the bihyperbolic numbers, we introduce new topologies on the bihyperbolic numbers set.

Suggested Citation

  • Ana Savić & Merve Bilgin & Soley Ersoy & Marija Paunović, 2022. "Topologies of Bihyperbolic Numbers," Mathematics, MDPI, vol. 10(22), pages 1-15, November.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:22:p:4224-:d:970545
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