-algebras of the monad -Fuzz
T-categories and some representation theorems
Tensor products of semilattices and distributive lattices.
The active bijection between regions and simplices in supersolvable arrangements of hyperplanes.
The algebra of pseudotopologies
The algebraic theory of compact Lawson semilattices Applications of Galois connections to compact semilattices [Book]
The alternation hierarchy for the theory of -lattices.
The amalgamation property of varieties determined by primitive lattices
The Cantor Extension of a Lexicographic Product of -Groups
The category of compactifications and its coreflections
We define “the category of compactifications”, which is denoted CM, and consider its family of coreflections, denoted corCM. We show that corCM is a complete lattice with bottom the identity and top an interpretation of the Čech–Stone . A corCM implies the assignment to each locally compact, noncompact a compactification minimum for membership in the “object-range” of . We describe the minimum proper compactifications of locally compact, noncompact spaces, show that these generate the atoms...
The characterization of -compact elements in some lattices
The dimension of a variety
Derived varieties were invented by P. Cohn in [4]. Derived varieties of a given type were invented by the authors in [10]. In the paper we deal with the derived variety of a given variety, by a fixed hypersubstitution σ. We introduce the notion of the dimension of a variety as the cardinality κ of the set of all proper derived varieties of V included in V. We examine dimensions of some varieties in the lattice of all varieties of a given type τ. Dimensions of varieties of lattices and all subvarieties...
The embedding of the formal concept analysis into the L-Fuzzy concept theory.
In this work, we study the relation between the concept lattice of Wille ([5], [6]) and the L-Fuzzy concept lattice ([2]) developed by us. To do it, we have defined an application g that associates to each concept of Wille an L-Fuzzy concept. The main point of this work is to prove that if we are working with a crisp relation between an object set and an attribute set, the concept lattice of Wille is a sublattice of the L-Fuzzy concept lattice. At the end, we show a typical example in the formal...
The existence of upper semicomplements in lattices of primitive classes
The facial structure of the finite dimensional latticial cone.
The free compact lattice generated by a topological semilattice.
The free lattice with 3 generators over
The graphs of join-semilattices and the shape of congruence lattices of particle lattices
We attach to each -semilattice a graph whose vertices are join-irreducible elements of and whose edges correspond to the reflexive dependency relation. We study properties of the graph both when is a join-semilattice and when it is a lattice. We call a -semilattice particle provided that the set of its join-irreducible elements satisfies DCC and join-generates . We prove that the congruence lattice of a particle lattice is anti-isomorphic to the lattice of all hereditary subsets of...
The ideal structure of simple ternary algebras
The integer sequence A002620 and upper antagonistic functions.