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On hyperballeans of bounded geometry

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Abstract

A ballean (or coarse structure) is a set endowed with some family of subsets, the balls, in such a way that balleans with corresponding morphisms can be considered as asymptotic counterparts of uniform topological spaces. For a ballean \({{\mathscr {B}}}\) on a set X, the hyperballean \({{\mathscr {B}}}^{\flat }\) is a ballean naturally defined on the set \(X^{\flat }\) of all bounded subsets of X. We describe all balleans with hyperballeans of bounded geometry and analyze the structure of these hyperballeans.

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Authors and Affiliations

  1. Department of Computer Science and Cybernetics, Kyiv University, Volodymyrska 64, Kyiv, 01033, Ukraine

    Igor Protasov & Ksenia Protasova

Authors
  1. Igor Protasov
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  2. Ksenia Protasova
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Correspondence to Igor Protasov.

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Protasov, I., Protasova, K. On hyperballeans of bounded geometry. European Journal of Mathematics 4, 1515–1520 (2018). https://doi.org/10.1007/s40879-018-0236-y

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  • DOI: https://doi.org/10.1007/s40879-018-0236-y

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