On probabilistic convergence rings and their natural uniform convergence structures
FILOMAT Journal of Mathematics
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 theorems om probabilistic convergence rings, (b) probabilistic uniformizabity of probabilistic limit rings, and discuss some results on probabilistic Cauchy rings, and their relationship with probabilistic convergence rings. In doing so, we produce various examples, particularly, from function space structure of continuous probabilistic convergence. Moreover, we observe that the category of probabilistic convergence ring in the sense of Richardson-Kent is a reflective subcategory of the category of probabilistic convergence rings in our sense.
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…