p-Topologicalness and p-regularity for lattice-valued convergence spaces

In this paper, p-topologicalness and p-regularity for Jägerʼs stratified L-generalized convergence spaces and those for Boustique et al.ʼs stratified L-convergence spaces are studied through two different methods. One method generalizes the well-known Fischerʼs (dual) diagonal condition, the other method uses the (neighborhood) closure of stratified L-filter. In addition, the p-topologicalness and p-regularity w.r.t. initial constructions and final constructions are also discussed.