STRATIFIED LATTICE-VALUED BALANCED NEIGHBORHOOD TOPOLOGICAL GROUPS

The aim of this article is to introduce the notion of stratified lattice-valued balanced neighborhood topological group. We also introduce the notions of equicontinuity in stratified lattice-valued neighborhood topological space, and uniform equicontinuity in stratified lattice-valued uniform space. We use these notions to characterize stratified lattice-valued neighborhood topological groups. Moreover, introducing the notions of lattice-valued neighborhood open function and lattice-valued uniformly open function, we show that in a stratified lattice-valued neighborhood topological group these notions are equivalent. Finally, we conclude with a characterization of balanced stratified lattice-valued neighborhood topological group in terms of uniform continuity of binary group operation.