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T M G Ahsanullah

Professor

Professor

كلية العلوم
Department of Mathematics, Building 4, Room No. 2B 80
publication
Journal Article
2022

On the probabilistic convergence spaces: Monad and its Eilenberg-Moore category by T. M. G. Ahsanullah, Tesnim Meryem Baran and Fawzi Al-Thukair

Ahsanullah, T. M. G. . 2022

Motivated by the category of probabilistic convergence spaces - a supercategory of the category of topological spaces, recently, we brought to light the categories of probabilistic convergence groups, probabilistic metric probabilistic convergence groups, probabilistic convergence transformation groups along with their underpinning natural examples. The purpose of this paper is, first, to establish a result on the isomorphism between the categories of probabilistic metric groups, and probabilistic metric probabilistic convergence groups. Secondly, among others, we explore various monads in relation with probabilistic convergence groups, and probabilistic convergence spaces, and their related algebras. In so doing, we consider a product of the categories of probabilistic convergence groups and probabilistic convergence spaces in an attempt to construct a monad on it such that the corresponding category of algebras, so-called Eilenberg-Moore category, is isomorphic to the category of probabilistic convergence transformation groups. Finally, invoking so-called Beck's theorem on characterization of algebras, and starting with a particular adjunction we achieved a monad; and, conversely, given a monad, we obtain an adjunction.
 

Publication Work Type
Original Research Article
Volume Number
18
Issue Number
2
Magazine \ Newspaper
New Math. & Nat. Comput. World Scientific
Pages
385 to 405
more of publication
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
publications

Starting with the category of probabilistic approach groups, we show that the category of approach groups can be embedded into the category of probabilistic approach groups as a bicoreflective…

by T M G Ahsanullah, Fawzi Al-Thukair and Bhamini Nayar
2023
publications

Starting with an approximation space as the underlying structure, we
look at the rough uniformity of a topological rough group. Next, taking L as a
complete residuated lattice, we…

by T M G Ahsanullah
2022
Published in:
Journal of Intelligent and Fuzzy Systems