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.
Funder
School of Electrical and Computer Engineering, Academy of Technical and Art Applied Studies
Subject
General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)
Reference41 articles.
1. On certain functions resembling Quaternions and on a new imaginary in algebra;Lond. Edinb. Dublin Philos. Mag. J. Sci.,1848
2. On a new imaginary in algebra;Lond. Edinb. Dublin Philos. Mag. J. Sci.,1849
3. On the symbols of algebra and on the theory of Tessarines;Lond. Edinb. Dublin Philos. Mag. J. Sci.,1849
4. Extending special relativity via the perplex numbers;Am. J. Phys.,1986
5. Rosenfeld, B. (1997). Geometry of Lie Groups, Kluwer Academic Publishers.