Protasov, Igor V.(Universitat Politècnica de València, 2008-10-01)
[EN] A ballean 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 the balleans can be considered as a natural asymptotic ...
Petrenko, Oleksandr; Protasov, Igor V.; Slobodianiuk, Sergii(Editorial Universitat Politècnica de València, 2014-10-01)
[EN] A ballean is a set X endowed with some family F of its subsets, called the balls, in such a way that (X,F) can be considered as an asymptotic counterpart of a uniform topological space. Given a cardinal k, we define ...
Protasov, Igor V.(Universitat Politècnica de València, 2007-10-01)
[EN] A ballean is a set X endowed with some family F of balls in such a way that a ballean can be considered as an asymptotic counterpart of a uniform topological space. Then we define the asymptotic counterparts for dense ...
Protasov, Igor V.(Universitat Politècnica de València, 2004-10-01)
[EN] A ball structure is a triple B = (X, P, B) where X, P are nonempty sets and, for any x ∈ X, α ∈ P, B(x, α) is a subset of X, which is called a ball of radius α around x. It is supposed that x ∈ B(x, α) for any x ∈ X, ...
Filali, Mahmoud; Protasov, Igor V.(Universitat Politècnica de València, 2008-10-01)
[EN] A ballean is a set endowed with some family of balls in such a way that a ballean can be considered as an asymptotic counterpart of a uniform topological space. We introduce and study a new cardinal invariant called ...
Protasov, Igor V.(Editorial Universitat Politècnica de València, 2013-10-01)
[EN] Let G be a group, PG be the family of all subsets of G. For a subset A ¿ G, we put ¿ (A) = {g ¿ G : |gA ¿ A| = ¿}. The mapping ¿ : PG ¿ PG, A ¿ ¿ (A), is called a combinatorial derivation and can be considered as an ...
Protasov, Igor V.; Slobodianiuk, Serhii(Universitat Politècnica de València, 2016-10-01)
[EN] We consider the action of a group $G$ on the family $\mathcal{P}(G)$ of all subsets of $G$ by the right shifts $A\mapsto Ag$ and give the dynamical characterizations of thin, $n$-thin, sparse and scattered subsets.For ...
Lutsenko, Ievgen; Protasov, Igor V.(Universitat Politècnica de València, 2010-10-01)
[EN] A ballean is a set endowed with some family of balls in such a way that a ballean can be considered as an asymptotic counterpar tof a uniform topological space. We characterize the ideal generated by the family of all ...