Thin subsets of balleans

Ievgen Lutsenko

Ukraine

Kyiv University

Departament of Cybernetics, Volodimirska 64, Kyiv, 01033, Ukraine

Igor V. Protasov

Ukraine

Kyiv University

Departament of Cybernetics

Submitted: 2013-09-24

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Accepted: 2013-09-24

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DOI: https://doi.org/10.4995/agt.2010.1710
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Keywords:

Ballean, Thin subsets, Ideal

Supporting agencies:

This research was not funded

Abstract:

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 thin subsets in an ordinal ballean, and apply this characterization to metric spaces and groups.
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References:

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M. Filali and I. V. Protasov, Spread of balleans, Appl. Gen. Topol. 9 (2008), 169–175.

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Ie. Lutsenko and I. V. Protasov, Sparse, thin and other subsets of groups, Internat. J. of Algebra Comput. 19 (2009), 491–510. http://dx.doi.org/10.1142/S0218196709005135

I. Protasov and M. Zarichnyi, General Asymptology, Math. Stud. Monogr. Ser., Vol. 11, VNTL Publishers, Lviv, 2007.

O. Protasova, Pseudodiscrete balleans, Algebra Discrete Math. 4 (2006), 81–92.

J. Roe, Lecture on Coarse Geometry, AMS University Lecture Ser. 31 (2003).

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