Convergence classes of \(L\)-filters in \((L, M)\)-fuzzy topological spaces (Q2052123)

Summary: An \((L, M)\)-fuzzy topological convergence structure on a set \(X\) is a mapping which defines a degree in \(M\) for any \(L\)-filter (of crisp degree) on \(X\) to be convergent to a molecule in \(L^X\). By means of \((L, M)\)-fuzzy topological neighborhood operators, we show that the category of \((L, M)\)-fuzzy topological convergence spaces is isomorphic to the category of \((L, M)\)-fuzzy topological spaces. Moreover, two characterizations of \(L\)-topological spaces are presented and the relationship with other convergence spaces is concretely constructed.