Abstract and concrete categories
Abstract and concrete categories
Pretopological and topological lattice-valued convergence spaces
Fuzzy Sets and Systems
Subcategories of lattice-valued convergence spaces
Fuzzy Sets and Systems
Compactification of lattice-valued convergence spaces
Fuzzy Sets and Systems
Compactness in lattice-valued function spaces
Fuzzy Sets and Systems
Fuzzy Sets and Systems
A one-point compactification for lattice-valued convergence spaces
Fuzzy Sets and Systems
Largest and smallest T2-compactifications of lattice-valued convergence spaces
Fuzzy Sets and Systems
Gähler's neighborhood condition for lattice-valued convergence spaces
Fuzzy Sets and Systems
Diagonal conditions for lattice-valued uniform convergence spaces
Fuzzy Sets and Systems
p-Topologicalness and p-regularity for lattice-valued convergence spaces
Fuzzy Sets and Systems
On (L,M)-fuzzy convergence spaces
Fuzzy Sets and Systems
Enriched lattice-valued convergence groups
Fuzzy Sets and Systems
| Hi-index | 0.21 |
We define a regularity axiom for lattice-valued convergence spaces where the lattice is a complete Heyting algebra. To this end, we generalize the characterization of regularity by a ''dual form'' of a diagonal condition. We show that our axiom ensures that a regular T1-space is separated and that regularity is preserved under initial constructions. Further we present an extension theorem for a continuous mapping from a subspace to a regular space. A characterization in the restricted case that the lattice is a complete Boolean algebra in terms of the closure of an L-filter is given.