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T M G Ahsanullah

Professor

Professor

كلية العلوم
Department of Mathematics, Building 4, Room No. 2B 80
publication
Journal Article
2025

On some subcategories of probabilistic convergence groups

In this article, we focus on discussing some subcategories of the category of probabilistic convergence groups, PConvGrp. In so doing, we introduce a category of probabilistic neighborhood spaces, PNeigh, and category of probabilistic topological spaces, PTopNeigh. We identify probabilistic metric spaces as probabilistic neighborhood spaces. Introducing a category of probabilistic neighborhood groups, PNeighGrp, and category of probabilistic topological neighborhood groups, PTopNeighGrp, we show that the category of probabilistic neighbor groups, PNeighGrp - a topological category, and the category of probabilistic pretopological groups, PPreTopGrp are isomorphic, and find a categorical relationship with categorical probabilistic neighborhood groups with probabilistic convergence groups. Furthermore, we introduce probabilistic pre Cauchy groups, PPreChyGrp, showing that the category of probabilistic Cauchy groups, a category previously introduced, is a full subcategory of PChyGrp. In this respect, we prove that in presence of probabilistic convergence groups, the category of probabilistic Cauchy groups, PChyGrp, the category of probabilistic strongly normal probabilistic limit groups, SNPLimitGrp are isomorphic. Moreover, following a notion of probabilistic normed group - a notion introduced earlier, we show that the category of probabilistic normed groups, PNormedGrp is isomorphic with the  category of probabilistic metric groups, PMetGrp. Finally, we present probabilistic version of so-called invariance of norm theorem.

 

Publication Work Type
Original Research
Publisher Name
European Journal of Pure and Applied Mathematics
Volume Number
18
Issue Number
3
Pages
1-28
more of publication
publications

In this article, we focus on discussing some subcategories of the category of probabilistic convergence groups, PConvGrp. In so doing, we introduce a category of probabilistic…

by T. M. G. Ahsanullah and Fawzi Al-Thukair
2025
Published in:
European Journal of Pure and Applied Mathematics
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In this paper, we present several characterizations on approach groups, and ultra-approach groups. In doing so, we first give necessary and sufficient conditions for an approach structure to be…

by T. M. G. Ahsanullah , Fawzi Al-Thukair
2024
Published in:
European Journal of Pure and Applied Mathematics
publications

Introducing the notion of probabilistic convergence ring, and probabilistic limit ring, our motivations among others are, to focus at two vital issues, such as, (a) to provide characterization…

by T. M. G. Ahsanullah and Gunther Jaeger
2024