Subcategories of probabilistic uniform convergence groups and probabilistic metrizability of probabilistic uniform convergence groups by T. M. G. Ahsanullah and Fawzi Al-Thukair
Ahsanullah, T. M. G. . 2019
We introduce categories of probabilistic uniform groups, PUGrp, and probabilistic uniform convergence groups, PUConvGrp; and show that there is an isomorphism between the category PUGrp and a subcategory of PUConvGrp. Considering an existing category of probabilistic uniform convergence spaces, we present a category of probabilistic uniform convergence groups by denoting it as N-PUConvGrp, and show that this category is a reflective subcategory of PUConvGrp. We observe that every probabilistic metric group gives rise to a probabilistic uniform group, and also, a probabilistic uniform convergence group in a natural way. Finally, we present a probabilistic metrization theorem on probabilistic uniform convergence group.
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…
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…