Several types of enriched ( L , M )-fuzzy convergence spaces

Cartesian-closedness and Subcategories of (L,M)-fuzzy Q-convergence Spaces

“…With the development of the theory of fuzzy topology [2,15,25,29], many types of fuzzy convergence structures have been proposed, such as stratified L-generalized convergence structure [9,11,17,18], Lfuzzifying convergence structure [26,27], L-convergence tower structure [8,10,22], L-ordered convergence structure [4,5], (Enriched) (L, M)-fuzzy (Q-)convergence structure [20,21,23], ⊺-convergence structure [6,12] and so forth. Fuzzy convergence structures are usually discussed from two aspects.…”

“…In this approach, Pang and Li showed the Cartesian-closedness of the categories of (L, M)-fuzzy convergence spaces [21] and L-fuzzy Q-convergence spaces [16], respectively. Later, Pang and Zhao [23] introduced the concept of stratified (L, M)-fuzzy Q-convergence spaces and proved that the resulting category is Cartesian closed. However, they failed to construct the corresponding function spaces.…”

“…However, they failed to construct the corresponding function spaces. By this motivation, we will focus on (L, M)-fuzzy Q-convergence spaces (called stratified (L, M)-fuzzy Q-convergence spaces in [23]) and present the concrete form of the corresponding function spaces. Moreover, we will introduce several types of (L, M)-fuzzy Q-convergence spaces and study their mutual relationships from a categorical aspect.…”

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

“…However, the lattice structure is used to replace the unit interval [0, 1] as the truth table for membership degrees. 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].…”

Degrees of separation properties in stratified L-generalized convergence spaces using residual implication

“…With the development of lattice-valued topology, many researchers extended convergence structures to the lattice-valued case and studied its categorical properties and topological properties, such as Jäger [8][9][10], Fang [2,3,28], Yao [29,30], Li [14,15], Pang [20][21][22][23][24][25]. In the situation of stratified L-topology, Min [19] proposed the concept of fuzzy convergence structures (called fuzzy limit structures in [19]) by using fuzzy prefilters and proved that the resulting category is Cartesian closed and can contain the category of stratified I-topological spaces as a reflective subcategory.…”