Complete Heyting algebra-valued convergence semigroups by T. M. G. Ahsanullah and Fawzi Al-Thukair
Ahsanullah, T M G . 2018
Considering a complete Heyting algebra $\mathbb{H}$, we introduce a notion of stratified $\mathbb{H}$-convergence semigroup. We develop some basic facts on the subject, besides obtaining conditions under which a stratified $\mathbb{H}$-convergence semigroup is a stratified $\mathbb{H}$-convergence group. We supply a variety of natural examples; and show that every stratified $\mathbb{H}$-convergence semigroup with identity is a stratified $\mathbb{H}$-quasi-uniform convergence space. We also show that given a commutative cancellative semigroup equipped with a stratified $\mathbb{H}$-quasi-unifom structure satisfying a certain property gives rise to a stratified $\mathbb{H}$-convergence semigroup via a stratified $\mathbb{H}$-quasi-uniform convergence structure.
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…