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.
Considering a value quantale, we introduce a category of quantale-valued convergence transformation groups on quantale-valued convergence spaces.
In this article, we focus on discussing some subcategories of the category of probabilistic convergence groups, PConvGrp. In so doing, we introduce a category of probabilistic…
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…