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Print ISSN: 2944-9162, E-ISSN: 2732-9941 An Open Access International Journal of Applied Science and Engineering
Volume 3, 2023
Topological Vector Spaces Derived From Topological Hypervector Spaces
Authors: , ,
Abstract: We introduce topological hypervector spaces on a topological field, in the sense of Tallini, and study some basic properties of this hyperspaces. In this regards we study the relationship between the topology on a hypervector spaces and its complete part. In particular we show that if every open subset of a topological hypervector space is a complete part then its fundamental vector space induced is a topological vector space. Finally, we study the quotient space of topological hypervector spaces and the derived topological space of a topological hypervector space with respect its fundamental relegation.
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Keywords: Topological hypervector space, Fundamental relation, Complete part, Topological fundamental vector space, Homeomorphism
Pages: 50-57
DOI: 10.37394/232020.2023.3.7