Pretopological and topological lattice-valued convergence spaces
Fuzzy Sets and Systems
On many-valued stratified L-fuzzy convergence spaces
Fuzzy Sets and Systems
Lattice-valued convergence spaces and regularity
Fuzzy Sets and Systems
Subcategories of lattice-valued convergence spaces
Fuzzy Sets and Systems
Stratified L-ordered convergence structures
Fuzzy Sets and Systems
Lattice-valued convergence spaces: Extending the lattice context
Fuzzy Sets and Systems
On stratified L-convergence spaces: Pretopological axioms and diagonal axioms
Fuzzy Sets and Systems
p-Topologicalness and p-regularity for lattice-valued convergence spaces
Fuzzy Sets and Systems
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We generalize a neighborhood condition from the category of convergence spaces to the category of lattice-valued convergence spaces. For a space in the category of convergence spaces, this condition is equivalent to being a topological space. It turns out that there are two meaningful generalizations of this condition to the category of lattice-valued convergence spaces. The first one guarantees that a space in a certain subcategory is a lattice-valued topological space. The other one is a levelwise condition which is equivalent to a generalization of Fischer's diagonal condition. The latter generalization is preserved under the embedding of the categories of convergence approach spaces and of probabilistic limit spaces into the category of lattice-valued convergence spaces.