Thin subsets of balleans

Authors

  • Ievgen Lutsenko Kyiv University
  • Igor V. Protasov Kyiv University

DOI:

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

Keywords:

Ballean, Thin subsets, Ideal

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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Author Biographies

Ievgen Lutsenko, Kyiv University

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

Igor V. Protasov, Kyiv University

Departament of Cybernetics

References

A. Bella and V. Malykhin, On certain subsets of groups, Questions Answers Gen. Topology 17 (1999), 183–187.

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

F. Harary, Graph Theory, Addison-Wesley Publ. Comp., 1969.

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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How to Cite

[1]
I. Lutsenko and I. V. Protasov, “Thin subsets of balleans”, Appl. Gen. Topol., vol. 11, no. 2, pp. 89–93, Oct. 2010.

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