Wehrung, Friedrich

We construct a completely normal bounded distributive lattice D in which for every pair (a, b) of elements, the set {x ∈ D | a ≤ b ∨ x} has a countable coinitial subset, such that D does not carry any binary operation - satisfying the identities x ≤ y ∨(x-y),(x-y)∧(y-x) = 0, and x-z ≤ (x-y)∨(y-z). In particular, D is not a homomorphic image of the ...

Wehrung, Friedrich

A compact topological space X is spectral if it is sober (i.e., every irreducible closed set is the closure of a unique singleton) and the compact open subsets of X form a basis of the topology of X, closed under finite intersections. Theorem. A topological space X is homeomorphic to the spectrum of some countable Abelian ℓ-group with unit (resp., ...

Barzegar, Hasan

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Das, Pratulananda Sengupta, Sayan Šupina, Jaroslav
Published in
Mathematica Slovaca

We continue to investigate the notion of IK ${\mathcal I}^{\mathcal K}$-convergence (which concerns with the convergence with respect to one ideal along a set which is “big” with respect to another ideal) introduced by M. Mačaj and M. Sleziak [10] with primary focus on sequences of real functions. Our investigation is based on results by R. Filipów...

Chodounský, David Repovš, Dušan Zdomskyy, Lyubomyr

We give topological characterizations of filters ▫$mathcal{F}$▫ on ▫$w$▫ such that the Mathias forcing ▫$M_mathcal{F}$▫ adds no dominating reals or preserves ground model unbounded families. This allows us to answer some questions of Brendle, Guzmán, Hrušák, Martínez, Minami, and Tsaban.

desclés, jean-pierre pascu, anca christine

. Finally, we show that the structural part of LTA can be modeled by a quasi topology structure (QTS).

Chajda, Ivan Länger, Helmut
Published in
Mathematica Slovaca

Basic algebras were introduced by Chajda, Halaš and Kühr as a common generalization of MV-algebras and orthomodular lattices, i.e. algebras used for formalization of non-classical logics, in particular the logic of quantum mechanics. These algebras were represented by means of lattices with section involutions. On the other hand, classical logic wa...

Ershov, Yu. L. Schwidefsky, M. V.
Published in
Siberian Mathematical Journal

We suggest an approach to advance the spectral theory of posets. The validity of the Hofmann-Mislove Theorem is established for posets and a characterization is obtained of the sober topological spaces as spectra of posets with topology. Also we describe the essential completions of topological spaces in terms of spectra of posets with topology. Ap...

ludkowski, sergey v.

This article is devoted to normed simple annihilator algebras. Their structure is investigated in the paper. Maximal families of orthogonal irreducible idempotents of normed simple annihilator algebras are scrutinized. Division subalgebras of annihilator algebras are studied. Realizations of these algebras by operator algebras in Banach spaces are ...

ludkowski, sergey v.

-algebras and finely regular algebras are also studied. Relations with operator theory and realizations of these algebras by operator algebras are outlined.