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.
In this paper, we present several characterizations on approach groups, and ultra-approach groups. In doing so, we first give necessary and sufficient conditions for an approach structure to be…
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…