p-Topologicalness and p-regularity for lattice-valued convergence spaces

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].…”

p-Regularity and p-Regular Modification in ⊤-Convergence Spaces

“…Quite recently, two types of fuzzy convergence spaces received wide attention: (1) stratified L-generalized convergence spaces (resp., stratified L-convergence spaces) initiated by Jäger [7] (resp., Flores [8]) and then developed by many scholars ; and (2) -convergence spaces introduced by Fang [31] and then discussed by many researchers [32][33][34][35][36]. Regularity in stratified L-generalized convergence spaces (resp., stratified L-convergence spaces) was studied by Jäger [37] (resp., Boustique-Richardson [38,39]), p-regularity and p-regular modifications in stratified L-generalized convergence spaces and that in stratified L-convergence spaces were discussed by Li [40,41]. Regularity in -convergence spaces by different diagonal conditions of -filters were researched by Fang [31] and Li [42], respectively.…”

A topology on lattice-ordered groups

“…Later, domain theory has got a great development in the areas of abstract theories of computation [28,32], the semantics of programming languages [29,34], logic and lambda calculus [3,33], and in other branches of mathematics [14,17]. Now, domain theory is still hot in lambda calculus and programming languages [1,2], stable domain theory [35,38], category theory [20,23], and has many applications in classical mathematics [18,25,26,30].…”