Balleans, hyperballeans and ideals

Authors

  • Dikran Dikranjan Università di Udine
  • Igor V. Protasov Kyiv University
  • Ksenia Protasova Kyiv University
  • Nicolò Zava Udine University

DOI:

https://doi.org/10.4995/agt.2019.11645

Keywords:

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

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.

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Author Biographies

Dikran Dikranjan, Università di Udine

Department of Mathematics and Computer Science

Igor V. Protasov, Kyiv University

Department of Computer Science and Cybernetics

Ksenia Protasova, Kyiv University

Department of Computer Science and Cybernetics

Nicolò Zava, Udine University

Department of Mathematics and Computer Science

References

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Published

2019-10-01

How to Cite

[1]
D. Dikranjan, I. V. Protasov, K. Protasova, and N. Zava, “Balleans, hyperballeans and ideals”, Appl. Gen. Topol., vol. 20, no. 2, pp. 431–447, Oct. 2019.

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Articles