The Infona portal uses cookies, i.e. strings of text saved by a browser on the user's device. The portal can access those files and use them to remember the user's data, such as their chosen settings (screen view, interface language, etc.), or their login data. By using the Infona portal the user accepts automatic saving and using this information for portal operation purposes. More information on the subject can be found in the Privacy Policy and Terms of Service. By closing this window the user confirms that they have read the information on cookie usage, and they accept the privacy policy and the way cookies are used by the portal. You can change the cookie settings in your browser.
We prove that every orthocomplete homogeneous effect algebra is sharply dominating. Let us denote the greatest sharp element below x by x↓. For every element x of an orthocomplete homogeneous effect algebra and for every block B with x ∈ B, the interval [x↓,x] is a subset of B. For every meager element (that means, an element x with x↓ = 0), the interval [0,x] is a complete MV-effect algebra. As...
Let r(n) denote the largest integer such that every family of n pairwise disjoint segments in the plane in general position has r(n) members whose order type can be represented by points. Pach and Tóth gave a construction that shows r(n) < nlog8/log9 (Pach and Tóth 2009). They also stated that one can apply the Erdős–Szekeres theorem for convex sets in Pach and Tóth (Discrete...
We study chains in an H-closed topological partially ordered space. We give sufficient conditions for a maximal chain L in an H-closed topological partially ordered space (H-closed topological semilattice) under which L contains a maximal (minimal) element. We also give sufficient conditions for a linearly ordered topological partially ordered space to be H-closed. We prove that a linearly ordered...
A finite poset F has the maximal antichain property if every maximal F-free subposet of every finite poset P contains a maximal antichain of P. We find all finite posets with the maximal antichain property.
We generalise some results of R. E. Stong concerning finite spaces to wider subclasses of Alexandroff spaces. In particular, we characterize pairs of spaces X,Y such that the compact-open topology on C(X,Y) is Alexandroff, give a homotopy type classification of a class of infinite Alexandroff spaces and prove some results concerning cores of locally finite spaces. We also discuss a mistake found in...
Let F be a partially ordered set (poset). A poset P is called F-free if P contains no subposet isomorphic to F. A finite poset F is said to have the maximal element property if every maximal F-free subposet of any finite poset P contains a maximal element of P. It is shown that a poset F with at least two elements has the maximal element property if and only if F is an antichain or F ≅ 2 + 2.
The smallest finitely based semigroup currently known to generate a variety with continuum many subvarieties is of order seven. The present article introduces a new example of order six and comments on the possibility of the existence of a smaller example. It is shown that if such an example exists, then up to isomorphism and anti-isomorphism, it must be a unique monoid of order five.
The classical way to study a finite poset (X, ≤ ) using topology is by means of the simplicial complex ΔX of its nonempty chains. There is also an alternative approach, regarding X as a finite topological space. In this article we introduce new constructions for studying X topologically: inspired by a classical paper of Dowker (Ann Math 56:84–95, 1952), we define the simplicial...
In Riesz space theory it is good practice to avoid representation theorems which depend on the axiom of choice. Here we present a general methodology to do this using pointfree topology. To illustrate the technique we show that Archimedean almost f-algebras are commutative. The proof is obtained relatively straightforward from the proof by Buskes and van Rooij by using the pointfree Stone-Yosida representation...
A synaptic algebra is an abstract version of the partially ordered Jordan algebra of all bounded Hermitian operators on a Hilbert space. We review the basic features of a synaptic algebra and then focus on the interaction between a synaptic algebra and its orthomodular lattice of projections. Each element in a synaptic algebra determines and is determined by a one-parameter family of projections—its...
This paper investigates quantum logic from the perspective of categorical logic, and starts from minimal assumptions, namely the existence of involutions/daggers and kernels. The resulting structures turn out to (1) encompass many examples of interest, such as categories of relations, partial injections, Hilbert spaces (also modulo phase), and Boolean algebras, and (2) have interesting categorical/logical/order-theoretic...
Let be the ordered set of isomorphism types of finite ordered sets (posets), where the ordering is by embeddability. We study first-order definability in this ordered set. We prove among other things that for every finite poset P, the set is definable, where p and are the isomorphism types of P and its dual poset. We prove...
Let G be a plane bipartite graph and ${\cal M}(G)$ the set of perfect matchings of G. A property that the Z-transformation digraph of perfect matchings of G is acyclic implies a partially ordered relation on ${\cal M}(G)$ . It was shown that ${\cal M}(G)$ is a distributive lattice if G is (weakly) elementary. Based on the unit decomposition of alternating cycle systems, in this article...
In his 1998 paper, Ryan classified the sets of unit, proper, and plain trapezoid and parallelogram orders. We extend this classification to include unit, proper, and plain triangle orders. We prove that there are 20 combinations of these properties that give rise to distinct classes of ordered sets, and order these classes by containment.
We present the numbers of all non-isomorphic residuated lattices with up to 12 elements and a link to a database of these lattices. In addition, we explore various characteristics of these lattices such as the width, length, and various properties considered in the literature and provide the corresponding statistics. We also present algorithms for computing finite residuated lattices including a fast...
We investigate the complexity of the lattice of local clones over a countably infinite base set. In particular, we prove that this lattice contains all algebraic lattices with at most countably many compact elements as complete sublattices, but that the class of lattices embeddable into the local clone lattice is strictly larger than that: For example, the lattice is a sublattice...
This paper is a contribution to the study of a quasi-order on the set Ω of Boolean functions, the simple minor quasi-order. We look at the join-irreducible members of the resulting poset . Using a two-way correspondence between Boolean functions and hypergraphs, join-irreducibility translates into a combinatorial property of hypergraphs. We observe that among Steiner systems, those...
We define NLC to be the restriction of the class of graphs NLCk, where relabelling functions are exclusively taken from a set of functions from {1,...,k} into {1,...,k}. We characterize the sets of functions for which NLC is well-quasi-ordered by the induced subgraph relation ≤ i. Precisely, these sets ...
Set the date range to filter the displayed results. You can set a starting date, ending date or both. You can enter the dates manually or choose them from the calendar.