By using some lattice-valued Kowalsky’s dual diagonal conditions, some weaker regularities for Jäger’s generalized stratified -convergence spaces and those for Boustique et al’s stratified -convergence spaces are defined and studied. Here, the lattice is a complete Heyting algebra. Some characterizations and properties of weaker regularities are presented. For Jäger’s generalized stratified -convergence spaces, a notion of closures of stratified -filters is introduced and then a new -regularity is defined. At last, the relationships between -regularities and weaker regularities are established.
"Lattice-Valued Convergence Spaces: Weaker Regularity and -Regularity." Abstr. Appl. Anal. 2014 1 - 11, 2014. https://doi.org/10.1155/2014/328153