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Перегляд Відділення математики за автором "Protasov, I."

Репозиторій DSpace/Manakin

Перегляд Відділення математики за автором "Protasov, I."

Сортувати за: Порядок: Результатів:

  • Coarse structures on groups defined by conjugations 
    Protasov, I.; Protasova, K. (Algebra and Discrete Mathematics, 2021)
  • 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 ...
  • Decompositions of set-valued mappings 
    Protasov, I. (Algebra and Discrete Mathematics, 2020)
  • 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 ...
  • On free vector balleans 
    Protasov, I.; Protasova, K. (Algebra and Discrete Mathematics, 2019)
    A vector balleans is a vector space over R endowed with a coarse structure in such a way that the vector operations are coarse mappings. We prove that, for every ballean (X, E), there exists the unique free vector ballean ...
  • On the subset combinatorics of G-spaces 
    Protasov, I.; Slobodianiuk, S. (Algebra and Discrete Mathematics, 2014)
    Let G be a group and let X be a transitive G-space. We classify the subsets of X with respect to a translation invariant ideal J in the Boolean algebra of all subsets of X, introduce and apply the relative combinatorical ...
  • 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 ...
  • Partitions of groups into sparse subsets 
    Protasov, I. (Algebra and Discrete Mathematics, 2012)
    A subset A of a group G is called sparse if, for every infinite subset X of G, there exists a finite subset F ⊂ X, such that ∩x∈FxA is finite. We denote by η(G) the minimal cardinal such that G can be partitioned in η(G) ...
  • Partitions of groups into thin subsets 
    Protasov, I. (Algebra and Discrete Mathematics, 2011)
    Let G be an infinite group with the identity e, κ be an infinite cardinal ≤|G|. A subset A⊂G is called κ-thin if |gA∩A|≤κ for every g∈G∖{e}. We calculate the minimal cardinal μ(G,κ) such that G can be partitioned in μ(G,κ) ...
  • Some more algebra on ultrafilters in metric spaces 
    Protasov, I. (Algebra and Discrete Mathematics, 2018)
    We continue algebraization of the set of ultrafilters on a metric spaces initiated in [6]. In particular, we define and study metric counterparts of prime, strongly prime and right cancellable ultrafilters from the Stone-Čech ...
  • The comb-like representations of cellular ordinal balleans 
    Protasov, I.; Protasova, K. (Algebra and Discrete Mathematics, 2016)
    Given two ordinal λ and γ, let f:[0,λ)→[0,γ) be a function such that, for each α<γ, sup{f(t):t∈[0,α]}<γ. We define a mapping df:[0,λ)×[0,λ)⟶[0,γ) by the rule: if x<y then df(x,y)=df(y,x)=sup{f(t):t∈(x,y]}, d(x,x)=0. The ...

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