Cellularity and density of balleans

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.