Balleans, hyperballeans and ideals

Dikran Dikranjan, Igor Protasov, Ksenia Protasova, Nicolò Zava

Abstract

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.


Keywords

balleans; coarse structure; coarse map; asymorphism; balleans defined by ideals; hyperballeans

Subject classification

54E15.

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References

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