Probabilistic uniformization and probabilistic metrization of probabilistic convergence groups by T. M. G. Ahsanullah and Gunther Jaeger
Ahsanullah, T. M. G. . 2017
We define probabilistic convergence groups based on Tardiff's neighborhood systems for probabilistic metric spaces and develop the basic theory. We study, as natural examples, probabilistic metric groups and probabilistic normed groups as well as probabilistic limit groups under a $t$-norm as defined earlier by the authors. We further show that a probabilistic convergence group induces a natural probabilistic uniform convergence structure and give a result on probabilistic metrization.
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 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…
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…