Subcategories of probabilistic uniform convergence groups and probabilistic metrizability of probabilistic uniform convergence groups

Journal Article
Al-Thukair, T. M. G. Ahsanullah, Fawzi . 2019
Publication Work Type: 
Original Research
Magazine \ Newspaper: 
Far East Journal of Mathematical Sciences
Issue Number: 
2
Volume Number: 
116
Pages: 
157 to 181
Publication Abstract: 

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.