TL;DR
This paper introduces the theory of topological modules over bicomplex numbers, exploring their convexity, seminorms, and conditions for normability and metrizability, advancing the mathematical framework of bicomplex analysis.
Contribution
It develops the foundational theory of topological bicomplex modules, including convexity, seminorms, and criteria for hyperbolic normability and metrizability.
Findings
Established conditions for hyperbolic normability.
Analyzed hyperbolic-valued seminorms and Minkowski functionals.
Explored convexity properties in bicomplex modules.
Abstract
In this paper, we develop topological modules over the ring of bicomplex numbers. We discuss bicomplex convexivity, hyperbolic-valued seminorms and hyperbolic-valued Minkowski functionals in bicomplex modules. We also study the conditions under which topological bicomplex modules and locally bicomplex convex modules become hyperbolic normable and hyperbolic metrizable respectively.
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