Spread of balleans

Authors

  • Mahmoud Filali University of Oulu
  • Igor V. Protasov Kyiv University

DOI:

https://doi.org/10.4995/agt.2008.1796

Keywords:

Ballean, Pseudodiscrete subset, Density, Cellularity, Spread

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 counterpart of a uniform topological space. We introduce and study a new cardinal invariant called the spread of a ballean. In particular, we show that, for every ordinal ballean B, spread of B coincides with density of B.

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Author Biographies

Mahmoud Filali, University of Oulu

Dept of Math. Sciences

Igor V. Protasov, Kyiv University

Department of Cybernetics

References

A. Dranishnikov, Asymptotic topology, Russian Math. Surveys 55 (2000), 1085–1129.

http://dx.doi.org/10.1070/RM2000v055n06ABEH000334

C. Chou, On the size of the set of left invariant means on a semigroup, Proc. Amer. Math. Soc. 23 (1969), 199–205.

I. V. Protasov, Normal ball structures, Math. Stud. 20 (2003), 3–16.

I. V. Protasov, Cellularity and density of balleans, Appl. Gen. Topology 8 (2007), 283–291.

I. V. Protasov and M. Zarichnyi, General Asymptology, Math. Stud. Monogr. Ser., VNTL, Lviv (2006).

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

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How to Cite

[1]
M. Filali and I. V. Protasov, “Spread of balleans”, Appl. Gen. Topol., vol. 9, no. 2, pp. 169–175, Oct. 2008.

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Articles