Stratified lattice-valued neighborhood tower group

Abstract

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

Mathematics Subject Classification (2010): 54A40, 54H11, 54B30

Keywords: Fuzzy topological group, lattice-valued topological group, L-neighborhood system, stratied L-neighborhood tower group