Lattice-valued quasi-bi-uniformizability of lattice-valued quasi-bi-topological neighborhood groups by T. M. G. Ahsanullah, Fawzi Al-Thukair and Jawaher Al-Mufarrij
Ahsanullah, T. M. G. . 2015
Considering a frame $L$, we introduce the notions of stratified $L$-semi-topological neighborhood group, stratified $L$-quasi-topological neighborhood group, and stratified $L$-quasi-bi-topological neighborhood group. In so doing, we look at the notion of stratified $L$-right (left) semi-topological neighborhood group, provide some basic facts, and present a construction of a stratified $L$-right semi-topological neighborhood group. We prove that every stratified $L$-quasi-bi-topological neighborhood group is $L$-quasi-bi-uniformizable; and finally, we present conditions under which a stratified $L$-quasi-topological neighborhood group is a stratified $L$-topological neighborhood group.
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…