Topologies of Bihyperbolic Numbers

Ana Savić, Merve Bilgin, Soley Ersoy and Marija Paunović ()
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Ana Savić: School of Electrical and Computer Engineering, Academy of Technical and Art Applied Studies, 11000 Belgrade, Serbia
Merve Bilgin: Department of Mathematics, Faculty of Sciences, University of Sakarya, 54050 Sakarya, Turkey
Soley Ersoy: Department of Mathematics, Faculty of Sciences, University of Sakarya, 54050 Sakarya, Turkey
Marija Paunović: Faculty of Hotel Management and Tourism, University of Kragujevac, 36210 Vrnjacka Banja, Serbia

Mathematics, 2022, vol. 10, issue 22, 1-15

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.

Keywords: bihyperbolic numbers; topology; semi-Euclidean space (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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