Frame valued stratified generalized convergence groups
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, S L-GCGrp is topological over the category of groups,Grp with respect to the forgetful functor, and we prove that the category S L-NeighGrp, of stratified L-neighborhood groups is isomorphic to a subcategory of S L-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.
This article gives results on fixed basis frame valued neighborhood topological groups and stratified neighborhood topological groups, includes some characterization theorems, and presents the…
Following the notion of stratified L-fuzzy convergence space of Gunther Jäger [Quaest.
The paper introduces and studies a new class of fuzzy open sets called j-fuzzy γI-open sets on fuzzy ideal topological spaces (FITSs).