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

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