Lattice-valued convergence spaces and regularity

On stratified L-convergence spaces: Fischer's diagonal axiom

“…That means, given a lattice-valued version of Fisher's diagonal axiom, one can obtain a corresponding notion of regularity of latticedvalued convergence spaces by dualizing that axiom. In particular, Jäger [12] postulated an axiom of lattice-valued regularity by making use of the dual axiom of (Lfw); in [17], the axioms (Lf), (Lfw) and (Lg) were generalized and employed to study the so called p-topologicalness and p-regularity of lattice-valued convergence spaces. So, it is natural to ask what happens if the axiom (Lfn) is dualized?…”

“…Stratified L-convergence spaces or stratified L-ordered convergence spaces, as a subcategory of stratified L-generalized convergence spaces, were proposed by Li in [14] and Fang in [3]. In recent years both of the spaces received much attention, see [3,4,[9][10][11][12][13][14][15][16][17][18][19]22].…”

On (L,M)-Double Fuzzy Filter Spaces

“…In recent years, -filters were used to introduce many kinds of lattice-valued convergence spaces [26][27][28]. -filter is an important tool to study -fuzzy topology [29,30] and -fuzzy uniform space [26].…”

On (L,M)-fuzzy convergence spaces

“…Using stratified L-filters, Jäger [9] introduced stratified L-fuzzy convergence spaces (which are called L-generalized convergence spaces in [10]) and proved that the category of topological stratified L-generalized convergence spaces and the category of stratified L-topological spaces are isomorphic. There are some following works to study the properties of this kind of fuzzy convergence structures [4,5,[11][12][13]16,17,25]. In the situation of L-fuzzifying topology, Xu [24] introduced fuzzifying convergence structures and proved that topological fuzzifying convergence structures and fuzzifying topologies are equivalent.…”