2013/10/07 by O. Petrenko, Petrenko, O., Ігор Протасов +4
Mathematics · #Advanced Topology and Set Theory #Homotopy and Cohomology in Algebraic Topology #Mathematical Dynamics and Fractals #math.CO #math.GN #msc:05A18 #msc:54A25
paper · pdf · doi:10.48550/arxiv.1310.1828
arxiv created 2013/10/07 · arxiv updated 2013/10/09
A ballean is a set X endowed with some family \F of its subsets, called the balls, in such a way that (X,\F) can be considered as an asymptotic counterpart of a uniform topological space. Given a cardinal κ, we define \F using a natural order structure on κ. We characterize balleans up to coarse equivalence, give the criterions of metrizability and cellularity, calculate the basic cardinal invariant of these balleans. We conclude the paper with discussion of some special ultrafilters on cardinal balleans.