Lattice-Valued Convergence Spaces: Weaker Regularity and p-Regularity

Abstract

By using some lattice-valued Kowalsky’s dual diagonal conditions, some weaker regularities for Jäger’s generalized stratified $L$-convergence spaces and those for Boustique et al’s stratified $L$-convergence spaces are defined and studied. Here, the lattice $L$ is a complete Heyting algebra. Some characterizations and properties of weaker regularities are presented. For Jäger’s generalized stratified $L$-convergence spaces, a notion of closures of stratified $L$-filters is introduced and then a new $p$-regularity is defined. At last, the relationships between $p$-regularities and weaker regularities are established.