Balleans, hyperballeans and ideals

[EN] A ballean B (or a coarse structure) on a set X is a family of subsets of X called balls (or entourages of the diagonal in X × X) dened in such a way that B can be considered as the asymptotic counterpart of a uniform topological space. The aim of this paper is to study two concrete balleans dened by the ideals in the Boolean algebra of all subsets of X and their hyperballeans, with particular emphasis on their connectedness structure, more specically the number of their connected components.The first named author thankfully acknowledges partial financial support via the grant PRID at the Department of Mathematical,Computer and Physical Sciences, Udine University.Dikranjan, D.; Protasov, I.; Protasova, K.; Zava, N. (2019). Balleans, hyperballeans and ideals. Applied General Topology. 20(2):431-447. https://doi.org/10.4995/agt.2019.11645SWORD43144720