Cellularity and density of balleans

Igor V. Protasov

Abstract

A ballean is a set X endowed with some family F of balls in such a way that a ballean can be considered as an asymptotic counterpart of a uniform topological space. Then we define the asymptotic counterparts for dense and open subsets, introduce two cardinal invariants (density and cellularity) of balleans and prove some results concerning relationship between these invariants. We conclude the paper with applications of obtained partitions of left topological group in dense subsets.

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1. Note: A conjecture on partitions of groups
Igor Protasov, Sergii Slobodianiuk
Combinatorica  vol: 36  issue: 3  first page: 365  year: 2016  
doi: 10.1007/s00493-014-3208-y



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Universitat Politècnica de València

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