Frame valued stratified generalized convergence groups

Abstract

Following the notion of stratified L-fuzzy convergence space of Gunther Jäger [Quaest. Math. 24 (2001), 501–517], we introduce the notion of a stratified L-generalized convergence group, and look into some other objects, namely, stratified L-Kent convergence groups, and stratified L-principal convergence groups. We show that the category of stratified L-generalized convergence groups, SL-GCGrp is topological over the category of groups, Grp with respect to the forgetful functor, and we prove that the category SL-NeighGrp, of stratified L-neighborhood groups is isomorphic to a subcategory of SL-GCGrp. We give necessary and sufficient conditions for a group structure and a stratified L-generalized convergence structure to be a stratified L-generalized convergence group. Finally, we observe that every stratified L-generalized convergence group possessing a stratified L-principal convergence structure gives rise to a stratified L-neighborhood topological group.

Keywords: Frame, stratified L-neighborhood space, stratified L-neighborhood topological space, stratified L-generalized convergence structure, stratified L-generalized convergence group, stratified L-Kent convergence group, stratified L-principal convergence group, stratified L-uniformity; topological category.

Quaestiones Mathematicae 31(2008), 279–302