Subcategories of lattice-valued convergence spaces (Q812556)

Let \(L\) be a complete Heyting algebra. A (stratified) \(L\)-filter on a set \(X\) is a function \(L^X\longrightarrow L\) with certain conditions. A stratified \(L\)-convergence structure on \(X\) is a function from the set of all stratified \(L\)-filters on \(X\) to \(L^X\). The author studies several subcategories of \(L\)-valued convergence spaces. These subcategories generalize the categories of Kent convergence spaces, limit spaces, pretopological spaces, and pseudotopological spaces to the Heyting algebra-valued setting.