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.
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