Asymptotic structures of cardinals


  • Oleksandr Petrenko Kyiv National University
  • Igor V. Protasov Kyiv University
  • Sergii Slobodianiuk Kyiv National University



cardinal balleans, coarse equivalence, metrizability, cellularity, cardinal invariants, ultrafilter.


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 k, we define F using a natural order structure on k. 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.


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How to Cite

O. Petrenko, I. V. Protasov, and S. Slobodianiuk, “Asymptotic structures of cardinals”, Appl. Gen. Topol., vol. 15, no. 2, pp. 137–146, Jul. 2014.