Lattice betweenness relation and a generalization of König's lemma
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 isomorphisms of alternative algebras
Lattice operators and topologies.
Lattice ordered groups with complete epimorphic images
Lattice separation, coseparation and regular measures.
Lattice uniformities on orthomodular structures
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 and semilattices having an antitone involution in every upper interval
We study -semilattices and lattices with the greatest element 1 where every interval [p,1] is a lattice with an antitone involution. We characterize these semilattices by means of an induced binary operation, the so called sectionally antitone involution. This characterization is done by means of identities, thus the classes of these semilattices or lattices form varieties. The congruence properties of these varieties are investigated.
Lattices freely generated by partially ordered sets: which can be "drawn"?
Lattices in quasiordered sets
Lattices of compatible relations
Lattices of convex equivalences
Lattices of fuzzy objects.
Lattices of generating systems
Lattices of lower finite breadth.
Lattices of order ideals on ordered semigroups.
Lattices of partially local Fitting classes.
Lattices of quasiorders on universal algebras
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...