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Completely Regular Semigroup Varieties A Comprehensive Study with Modern Insights
This book is a unified treatment of the most important core developments in the theory of completely regular semigroup theory as it stands today....
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On Extension of Multilinear Operators and Homogeneous Polynomials in Vector Lattices
We establish the existence of a simultaneous extension from a majorizing sublattice in the classes of regular multilinear operators and...
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Two Flags in a Semimodular Lattice Generate an Antimatroid
A basic property in a modular lattice is that any two flags generate a distributive sublattice. It is shown (Abels 1991, Herscovici 1998) that two...
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Order continuity and regularity on vector lattices and on lattices of continuous functions
We give several characterizations of order continuous vector lattice homomorphisms between Archimedean vector lattices. We reduce the proofs of some...
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Lattices
In Chapter 2, we briefly introduced lattices in the Euclidean space $$\mathbb...
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The coarsest lattice that determines a discrete multidimensional system
A discrete multidimensional system is the set of solutions to a system of linear partial difference equations defined on the lattice
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On the symmetric parts of finitely generated free lattices
An element of finitely generated free lattices is called symmetric if it is fixed by all automorphisms of the lattice. We examine the lattice...
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A property of meets in slim semimodular lattices and its application to retracts
Slim semimodular lattices were introduced by G. Grätzer and E. Knapp in 2007, and they have intensively been studied since then. These lattices can...
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The Lattice NExtS41 as Composed of Replicas of NExtInt, and Beyond
We study the lattice of all normal consistent extensions of the modal logic...
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Pervin Spaces and Frith Frames: Bitopological Aspects and Completion
A Pervin space is a set equipped with a bounded sublattice of its powerset, while its pointfree version, called Frith frame, consists of a frame...
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A Study of the Small Inductive Dimension in the Area of Finite Lattices
The Dimension Theory in the class of frames was the base of many researches. Especially, the covering dimension, the quasi covering dimension, the...
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Convergence structures and Hausdorff uo-Lebesgue topologies on vector lattice algebras of operators
A vector sublattice of the order bounded operators on a Dedekind complete vector lattice can be supplied with the convergence structures of order...
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A STONE-WEIERSTRASS-TYPE THEOREM FOR TRUNCATED VECTOR LATTICES OF FUNCTIONS
A nonempty set S of real-valued functions is said to be truncated if it contains with any function f its meet with the constant function 1. Very...
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A Godefroy—Kalton principle for free Banach lattices
Motivated by the Lipschitz-lifting property of Banach spaces introduced by Godefroy and Kalton, we consider the lattice-lifting property, which is an...
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Representations for the Largest Extension of a Closure System
An extension of a closure system on a finite set S is a closure system on the same set S containing the first one as a sublattice. A closure system...