Spread of balleans

Mahmoud Filali

Finland

University of Oulu

Dept of Math. Sciences

Igor V. Protasov

Ukraine

Kyiv University

Department of Cybernetics

Submitted: 2013-10-30

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Accepted: 2013-10-30

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

Ballean, Pseudodiscrete subset, Density, Cellularity, Spread

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 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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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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