Stratified lattice-valued neighborhood tower group

Abstract

In this paper, by generalizing Höhle and Šostak’s stratified L-fuzzy neighborhood system, the notion of stratified L-neighborhood tower space is introduced. Then by enriching a group structure on a stratified L-neighborhood tower space, the notion of stratified L-neighborhood tower group is proposed. It is proved that this notion can be regarded as a natural extension of stratified L-neighborhood group dis- cussed by Ahsanullah etal. Indeed, the category of stratified L-neighborhood tower groups includes the category of stratified L-neighborhood groups as a concretely reflective (resp., coreflective) full subcategory. Furthermore, it is shown that the group operations enrich a stratified L-neighborhood tower space to be topological (generally, stratified L-neighborhood tower space is not topological). This means that there is no difference between stratified L-neighborhood tower group and topologically stratified L-neighborhood tower group.