Complete Heyting algebra-valued convergence semigroups

Journal Article

Al-Thukair, T M G Ahsanullah and Fawzi . 2018

• Publication Work Type: Original Reserach
• Magazine \ Newspaper: Filomat
• Volume Number: Accepted, to appear in 2018

Publication Abstract

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.