Перегляд за автором "Protasov, I.V."

Сортувати за: Порядок: Результатів:

  • Algebra in the Stone-Čech compactification: applications to topologies on groups 
    Protasov, I.V. (Algebra and Discrete Mathematics, 2009)
    For every discrete group G, the Stone-Čech compactification βG of G has a natural structure of compact right topological semigroup. Assume that G is endowed with some left invariant topology I and let τ¯ be the set of all ...
  • Automorphisms of kaleidoscopical graphs 
    Protasov, I.V.; Protasova, K.D. (Algebra and Discrete Mathematics, 2007)
    A regular connected graph Γ of degree s is called kaleidoscopical if there is a (s + 1)-coloring of the set of its vertices such that every unit ball in Γ has no distinct monochrome points. The kaleidoscopical graphs can ...
  • Balleans and G-spaces 
    Petrenko, O.V.; Protasov, I.V. (Український математичний журнал, 2012)
    We show that every ballean (equivalently, coarse structure) on a set X can be determined by some group G of permutations of X and some group ideal I on G. We refine this characterization for some basic classes of balleans ...
  • Balleans of bounded geometry and G-spaces 
    Protasov, I.V. (Algebra and Discrete Mathematics, 2008)
    A ballean (or a coarse structure) is a set endowed with some family of subsets which are called the balls. The properties of the family of balls are postulated in such a way that a ballean can be considered as an asymptotical ...
  • Balleans of topological groups 
    Hernández, S.; Protasov, I.V. (Український математичний вісник, 2011)
    A subset S of a topological group G is called bounded if, for every neighborhood U of the identity of G, there exists a finite subset F such that S ⊆ FU, S ⊆ UF. The family of all bounded subsets of G determines two ...
  • Binary coronas of balleans 
    Protasov, I.V. (Algebra and Discrete Mathematics, 2003)
    A ballean B is a set X endowed with some family of subsets of X which are called the balls. We postulate the properties of the family of balls in such a way that a ballean can be considered as an asymptotic counterpart ...
  • Coarse rays 
    Kuchaiev, O.; Protasov, I.V. (Український математичний вісник, 2008)
    We give some characterizations of geodesic metric spaces coarsely equivalent to the ray R⁺.
  • Color-detectors of hypergraphs 
    Protasov, I.V.; Protasova, O.I. (Algebra and Discrete Mathematics, 2005)
    Let X be a set of cardinality k, F be a family of subsets of X. We say that a cardinal λ,λ<k, is a color-detector of the hypergraph H=(X,F) if card χ(X)≤λ for every coloring χ:X→k such that card χ(F)≤λ for every F∈F. ...
  • Discontinuous Birkhoff theorem 
    Petrenko, O.; Protasov, I.V. (Український математичний вісник, 2007)
    A topological space X is called totally recurrent if every mapping f : X → X has a recurrent point. We prove that a Hausdorff space X is totally recurrent if and only if X is either finite or a one-point compactification ...
  • Metrizable ball structures 
    Protasov, I.V. (Algebra and Discrete Mathematics, 2002)
    A ball structure is a triple (X, P, B), where X, P are nonempty sets and, for any x ∈ X, α ∈ P, B(x, α) is a subset of X, x ∈ B(x, α), which is called a ball of radius α around x. We characterize up to isomorphism the ...
  • Morphisms of Ball's Structures of Groups and Graphs 
    Protasov, I.V. (Український математичний журнал, 2002)
    We introduce and study two kinds of morphisms between ball's structures related to groups and graphs.
  • On n-stars in colorings and orientations of graphs 
    Protasov, I.V. (Algebra and Discrete Mathematics, 2016)
    An n-star S in a graph G is the union of geodesic intervals I1,…,Ik with common end O such that the subgraphs I1∖{O},…,Ik∖{O} are pairwise disjoint and l(I1)+…+l(Ik)=n. If the edges of G are oriented, S is directed if each ...
  • On recurrence in G-spaces 
    Protasov, I.V.; Protasova, K.D. (Algebra and Discrete Mathematics, 2017)
    We introduce and analyze the following general concept of recurrence. Let G be a group and let X be a G-space with the action G×X⟶X, (g,x)⟼gx. For a family F of subset of X and A∈F, we denote ΔF(A)={g∈G:gB⊆A for some B∈F, ...
  • Prethick subsets in partitions of groups 
    Protasov, I.V.; Slobodianiuk, S. (Algebra and Discrete Mathematics, 2012)
    A subset S of a group G is called thick if, for any finite subset F of G, there exists g ∈ G such that Fg ⊆ S, and k-prethick, k ∈ N if there exists a subset K of G such that |K| = k and KS is thick. For every finite ...
  • Recent progress in Subset Combinatorics of Groups 
    Protasov, I.V.; Protasova, K.D. (Український математичний вісник, 2017)
    We systematize and analyze some results obtained in Subset Combinatorics of G groups after publications the previous surveys [1–4]. The main topics: the dynamical and descriptive characterizations of subsets of a group ...
  • Relatively thin and sparse subsets of groups 
    Lutsenko, Ie.; Protasov, I.V. (Український математичний журнал, 2011)
    Let G be a group with identity e and let I be a left-invariant ideal in the Boolean algebra PG of all subsets of G. A subset A of G is called I-thin if gA⋂A∈I for every g∈G {e}. A subset A of G is called I-sparse if, for ...
  • Scattered Subsets of Groups 
    Banakh, T.O.; Protasov, I.V.; Slobodianiuk, S.V. (Український математичний журнал, 2015)
    We define scattered subsets of a group as asymptotic counterparts of the scattered subspaces of a topological space and prove that a subset A of a group G is scattered if and only if A does not contain any piecewise shifted ...
  • Selective survey on Subset Combinatorics of Groups 
    Protasov, I.V. (Український математичний вісник, 2010)
    We survey recent results concerning the combinatorial size of subsets of groups. For a cardinal k, according to its arrangement in a group G, a subset of G is distinguished as k-large, k-small, k-thin, k-thick and Pk-small. ...
  • Thin Subsets of Groups 
    Protasov, I.V.; Slobodyanyuk, S. (Український математичний журнал, 2013)
    For a group G and a natural number m, a subset A of G is called m-thin if, for each finite subset F of G, there exists a finite subset K of G such that |Fg ∩ A| ≤ m for all g ∈ G \ K. We show that each m-thin subset of an ...
  • Ultrafilters on balleans 
    Protasov, I.V.; Slobodianiuk, S.V. (Український математичний журнал, 2015)
    A ballean (equivalently, a coarse structure) is an asymptotic counterpart of a uniform space. We introduce three ultrafilter satellites of a ballean (namely, corona, companion, and corona companion), evaluate the basic ...