Lattice-valued quasi-bi-uniformizability of lattice-valued quasi-bi-topological neighborhood groups

Journal Article

Al-Mufarij, Ahsanullah, T.M. G., Fawzi Al-Thukair, Jawaher . 2015

• Publication Work Type: Original Research
• Publication Online URL: International Journal of Contemporary Mathematical Sciences
• Issue Number: 6
• Volume Number: 10
• Pages: 253-268

Publication Abstract

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.