Inversions on complete lattices and Girard quantales
Irreducibility and generation in continuous lattices.
Join-closed and meet-closed subsets in complete lattices
To every subset of a complete lattice we assign subsets , and define join-closed and meet-closed sets in . Some properties of such sets are proved. Join- and meet-closed sets in power-set lattices are characterized. The connections about join-independent (meet-independent) and join-closed (meet-closed) subsets are also presented in this paper.
Lattice effect algebras densely embeddable into complete ones
An effect algebraic partial binary operation defined on the underlying set uniquely introduces partial order, but not conversely. We show that if on a MacNeille completion of there exists an effect algebraic partial binary operation then need not be an extension of . Moreover, for an Archimedean atomic lattice effect algebra we give a necessary and sufficient condition for that existing on is an extension of defined on . Further we show that such extending exists at most...
Lattice ordered groups with complete epimorphic images
Lattice-inadmissible incidence structures
Join-independent and meet-independent sets in complete lattices were defined in [6]. According to [6], to each complete lattice (L,≤) and a cardinal number p one can assign (in a unique way) an incidence structure of independent sets of (L,≤). In this paper some lattice-inadmissible incidence structures are founded, i.e. such incidence structures that are not isomorphic to any incidence structure .
Lattices of compatible relations
Lattices of convex equivalences
Lattices of fuzzy objects.
Lattices of Scott-closed sets
A dcpo is continuous if and only if the lattice of all Scott-closed subsets of is completely distributive. However, in the case where is a non-continuous dcpo, little is known about the order structure of . In this paper, we study the order-theoretic properties of for general dcpo’s . The main results are: (i) every is C-continuous; (ii) a complete lattice is isomorphic to for a complete semilattice if and only if is weak-stably C-algebraic; (iii) for any two complete semilattices...
Lattices of tolerances
Left and right semi-uninorms on a complete lattice
Uninorms are important generalizations of triangular norms and conorms, with a neutral element lying anywhere in the unit interval, and left (right) semi-uninorms are non-commutative and non-associative extensions of uninorms. In this paper, we firstly introduce the concepts of left and right semi-uninorms on a complete lattice and illustrate these notions by means of some examples. Then, we lay bare the formulas for calculating the upper and lower approximation left (right) semi-uninorms of a binary...
Localic groups
-poproduct of lattices
Maximal completion of a pseudo MV-algebra
In the present paper we investigate the relations between maximal completions of lattice ordered groups and maximal completions of pseudo -algebras.
Metric-fine uniform frames
A locallic version of Hager’s metric-fine spaces is presented. A general definition of -fineness is given and various special cases are considered, notably all metric frames, complete metric frames. Their interactions with each other, quotients, separability, completion and other topological properties are discussed.
Multiplicative structures over sup-lattices
Negaciones en retículos completos.
Note on algebraic interior systems
We get an interrelation between an algebraic closure system and its conjugated interior system. We introduce the concept of algebraic interior system and we get its representation.
Note on dense covers in the category of locales
In this note we are going to study dense covers in the category of locales. We shall show that any product of finitely regular locales with some dense covering property has this property as well.