Intrinsic topologies on semilattices of finite breadth.
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...
Metrizable completely distributive lattices
The purpose of this paper is to study the topological properties of the interval topology on a completely distributive lattice. The main result is that a metrizable completely distributive lattice is an ANR if and only if it contains at most finite completely compact elements.
Notes on lattices of frame tolerances
On central relations of complete lattices
On imaginable -fuzzy subalgebras and imaginable -fuzzy closed ideals in BCH-algebras.
On minimal spectrum of multiplication lattice modules
We study the minimal prime elements of multiplication lattice module over a -lattice . Moreover, we topologize the spectrum of minimal prime elements of and study several properties of it. The compactness of is characterized in several ways. Also, we investigate the interplay between the topological properties of and algebraic properties of .
On pushing out frames
On Raney's theorems for completely distributive complete lattices
On the lattice of additive hereditary properties of finite graphs
In this paper it is proved that the lattice of additive hereditary properties of finite graphs is completely distributive and that it does not satisfy the Jordan-Dedekind condition for infinite chains.
One-variable equationally compact distributive lattices
Overtaker binary relations on complete completely distributive lattices related to the level sets of the L-Fuzzy sets.
The class of overtaker binary relations associated with the order in a lattice is defined and used to generalize the representations of L-fuzzy sets by means of level sets or fuzzy points.
Pointless uniformities. I. Complete regularity
Pointless uniformities. II: (Dia)metrization
Prime ideals in the lattice of additive induced-hereditary graph properties
An additive induced-hereditary property of graphs is any class of finite simple graphs which is closed under isomorphisms, disjoint unions and induced subgraphs. The set of all additive induced-hereditary properties of graphs, partially ordered by set inclusion, forms a completely distributive lattice. We introduce the notion of the join-decomposability number of a property and then we prove that the prime ideals of the lattice of all additive induced-hereditary properties are divided into two groups,...
Primes, coprimes and multiplicative elements
The purpose of this paper is to study conditions under which the restriction of a certain Galois connection on a complete lattice yields an isomorphism from a set of prime elements to a set of coprime elements. An important part of our study involves the set on which the way-below relation is multiplicative.
Radical classes of distributive lattices having the least element
Let be the system of all distributive lattices and let be the system of all such that possesses the least element. Further, let be the system of all infinitely distributive lattices belonging to . In the present paper we investigate the radical classes of the systems , and .
Split structures.
Standard completions for quasiordered sets.
Sublattices of Euclidean spaces.