Related papers: Conjunctive Join Semi-Lattices
Let $C(X,I)$ be the lattice of all continuous functions on a compact Hausdorff space $X$ with values in the unit interval $I=[0,1]$. We show that for compact Hausdorff spaces $X$ and $Y$ and (not necessarily contain constants) sublattices…
We characterize numerical semigroups for which the poset of its ideal class monoid is a lattice, and study the irreducible elements of such a lattice with respect to union, intersection, infimum and supremum.
The purpose of this article is to investigate the combinatorial properties of the cross section lattice of a $J$-irreducible monoid associated with a semisimple algebraic group of one of the types $A_n$, $B_n$, or $C_n$. Our main tool is a…
Motivated by Gentzen disjunction elimination rule in his Natural Deduction calculus and reading inequalities with meet in a natural way, we conceive a notion of distributivity for join-semilattices. We prove that it is equivalent to a…
We discuss the relationship between tight and cover-to-join representations of semilattices and inverse semigroups, showing that a slight extension of the former, together with an appropriate selection of co-domains, makes the two notions…
Given a semigroup $S$ and $s,t \in S$, write $s \sim_p^1 t$ if $s=pr$ and $t=rp$, for some $p,r \in S \cup \{1\}$. This relation, known as "primary conjugacy", along with its transitive closure $\sim_p$, has been extensively used and…
We begin with a short exposition of the theory of lattice varieties. This includes a description of their orbit structure and smooth locus. We construct a flat cover of the lattice variety and show that it is a complete intersection. We…
We introduce a pointfree theory of convergence on lattices and coframes. A convergence lattice is a lattice $L$ with a monotonic map $\lim_L$ from the lattice of filters on $L$ to $L$, meant to be an abstract version of the map sending…
Dedekind stated and proved the well-known fact that a lattice is modular if and only if it does not contain a pentagon as a sublattice. In this paper we consider a similar result in the literature for the case of certain class of modular…
Let $\F$ be an algebraically closed field. Let $\V$ be a vector space equipped with a non-degenerate symmetric or symplectic bilinear form $B$ over $\F$. Suppose the characteristic of $\F$ is \emph{large}, i.e. either zero or greater than…
We show that a linearly ordered topological space is initially \lambda-compact if and only if it is \lambda-bounded, that is, every set of cardinality $\leq \lambda$ has compact closure. As a consequence, every product of initially…
The Sasaki projection was introduced as a mapping from the lattice of closed subspaces of a Hilbert space onto one of its segments. To use this projection and its dual so-called Sasaki operations were introduced by the second two authors.…
The canonical join complex of a semidistributive lattice is a simplicial complex whose faces are canonical join representations of elements of the semidistributive lattice. We give a combinatorial classification of the faces of the…
Duistermaat introduced the concept of ``real locus'' of a Hamiltonian manifold. In that and in others' subsequent works, it has been shown that many of the techniques developed in the symplectic category can be used to study real loci, so…
Composition and lattice join (transitive closure of a union) of equivalence relations are operations taking pairs of decidable equivalence relations to relations that are semi-decidable, but not necessarily decidable. This article addresses…
We investigate the lattice L(V) of subspaces of an m-dimensional vector space V over a finite field GF(q) with q being the n-th power of a prime p. It is well-known that this lattice is modular and that orthogonality is an antitone…
We consider some distinguished classes of elements of a multiplicative lattice endowed with coarse lower topologies, and call them lower spaces. The primary objective of this paper is to study the topological properties of these lower…
A semigroup conjugacy is an equivalence relation that equals group conjugacy when the semigroup is a group. In this note, we answer five open problems related to semigroup conjugacy. (Problem One) We say a conjugacy ~ is partition-covering…
Properties of several sorts of lattices of convex subsets of R^n are examined. The lattice of convex sets containing the origin turns out, for n>1, to satisfy a set of identities strictly between those of the lattice of all convex subsets…
Slim semimodular lattices were introduced by G. Gr\"atzer and E. Knapp in 2007, and they have intensively been studied since then. It is often reasonable to give these lattices by their $\mathcal C_1$-diagrams defined by the author in 2017.…