Spread of balleans

Mahmoud Filali, Igor V. Protasov


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.


Ballean; Pseudodiscrete subset; Density; Cellularity; Spread

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


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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1. Asymptotic structures of cardinals
Oleksandr Petrenko, Igor V. Protasov, Sergii Slobodianiuk
Applied General Topology  vol: 15  issue: 2  first page: 137  year: 2014  
doi: 10.4995/agt.2014.3109

Esta revista se publica bajo una licencia de Creative Commons Reconocimiento-NoComercial-SinObraDerivada 4.0 Internacional.

Universitat Politècnica de València

e-ISSN: 1989-4147   https://doi.org/10.4995/agt