Gähler's neighborhood condition for lattice-valued convergence spaces

p-Topologicalness—A Relative Topologicalness in ⊤-Convergence Spaces

“…Let (X, lim p ) be a stratified L-generalized convergence space. For any 29]. We say a pair of stratified L-generalized convergence spaces (X, lim p , lim q ) satisfy the Fischer L-diagonal condition if p-(LF): Let J, X be any sets, Ψ : J −→ X and Φ :…”

“…In recent years, two kinds of lattice-valued convergence spaces received much attention: (1) the theory of stratified L-generalized convergence spaces based on L-filters, which is initiated by Jäger [5] and then developed by many researchers [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25]; and (2) the theory of -convergence spaces based on -filters, which is investigated by Fang [26] in 2017. The topologicalness in stratified L-generalized convergence spaces was studied by Jäger [27][28][29] and Li [30,31], the p-topologicalness and p-topological modifications in stratified L-generalized convergence spaces were discussed by Li [32,33].…”

Convergence Classes of L -Filters in L , M -Fuz

“…Jäger also gave some kinds of characterizations of stratified L-topological spaces (see [6,[9][10][11]). With the help of Jäger's work, Li [12] proved that there is a one-to-one correspondence between the set of all convergence functions of specific L-fuzzy filters on X and the set of all specific L-topologies on X for L, a complete residual lattice.…”

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

“…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].…”