Перегляд за автором "Banakh, T."

Сортувати за: Порядок: Результатів:

  • Algebra in superextensions of groups, II: cancelativity and centers 
    Banakh, T.; Gavrylkiv, V. (Algebra and Discrete Mathematics, 2008)
    Given a countable group X we study the algebraic structure of its superextension λ(X). This is a right-topological semigroup consisting of all maximal linked systems on X endowed with the operation A∘B={C⊂X:{x ...
  • Algebra in superextensions of inverse semigroups 
    Banakh, T.; Gavrylkiv, V. (Algebra and Discrete Mathematics, 2012)
    We find necessary and sufficient conditions on an (inverse) semigroup X under which its semigroups of maximal linked systems λ(X), filters φ(X), linked upfamilies N₂(X), and upfamilies υ(X) are inverse.
  • Algebra in superextensions of semilattices 
    Banakh, T.; Gavrylkiv, V. (Algebra and Discrete Mathematics, 2012)
    Given a semilattice X we study the algebraic properties of the semigroup υ(X) of upfamilies on X. The semigroup υ(X) contains the Stone-ˇCech extension β(X), the superextension λ(X), and the space of filters φ(X) on X as ...
  • Characterizing semigroups with commutative superextensions 
    Banakh, T.; Gavrylkiv, V. (Algebra and Discrete Mathematics, 2014)
    We characterize semigroups X whose semigroups of filters φ(X), maximal linked systems λ(X), linked upfamilies N₂(X), and upfamilies υ(X) are commutative.
  • Completeness of invariant ideals in groups 
    Banakh, T.; Lyakovska, N. (Український математичний журнал, 2010)
    We introduce and study various notions of completeness of translation-invariant ideals in groups.
  • Constructing balleans 
    Banakh, T.; Protasov, I. (Український математичний вісник, 2018)
    A ballean is a set endowed with a coarse structure.We introduce and explore three constructions of balleans from a pregiven family of balleans: bornological products, bouquets, and combs. We analyze also the smallest and ...
  • Densities, submeasures and partitions of groups 
    Banakh, T.; Protasov, I.; Slobodianiuk, S. (Algebra and Discrete Mathematics, 2014)
    In 1995 in Kourovka notebook the second author asked the following problem: is it true that for each partition G=A₁ ∪ ⋯ ∪ An of a group G there is a cell Ai of the partition such that G = FAiA⁻¹i for some set F ⊂ G of ...
  • Descriptive classes of sets and topological functors 
    Banakh, T. (Український математичний журнал, 1995)
    It is proved that the image of a normal functor from the Stone-Cech compactification of the projective class of sets also belongs to this class.
  • On subgroups of saturated or totally bounded paratopological groups 
    Banakh, T.; Ravsky, S. (Algebra and Discrete Mathematics, 2003)
    A paratopological group G is saturated if the inverse U ⁻¹ of each non-empty set U ⊂ G has non-empty interior. It is shown that a [first-countable] paratopological group H is a closed subgroup of a saturated (totally ...
  • Partitions of groups and matroids into independent subsets 
    Banakh, T.; Protasov, I. (Algebra and Discrete Mathematics, 2010)
    Can the set R∖{0} be covered by countably many linearly (algebraically) independent subsets over the field Q? We use a matroid approach to show that an answer is ``Yes'' under the Continuum Hypothesis, and ``No'' under its ...
  • Weakly P-small not P-small subsets in Abelian groups 
    Banakh, T.; Lyaskovska, N. (Algebra and Discrete Mathematics, 2006)
    Answering a question of D. Dikranjan and I. Protasov we prove that each infinite Abelian group contains a weakly P-small subset that is not P-small.
  • Zero-sum subsets of decomposable sets in Abelian groups 
    Banakh, T.; Ravsky, A. (Algebra and Discrete Mathematics, 2020)
    A subset D of an abelian group is decomposable if ∅ ≠ D ⊂ D + D. In the paper we give partial answers to an open problem asking whether every finite decomposable subset D of an abelian group contains a non-empty subset ...