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

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.