Lattice-valued convergence spaces: weaker regularity and \(p\)-regularity
Summary: 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.
scientific article; zbMATH DE number 7022180
scientific article