Asymptotic structures of cardinals

Oleksandr Petrenko

Ukraine

Kyiv National University

Igor V. Protasov

Ukraine

Kyiv University

Sergii Slobodianiuk

Ukraine

Kyiv National University

Submitted: 2014-06-19

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Accepted: 2014-06-19

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Published: 2014-07-15

DOI: https://doi.org/10.4995/agt.2014.3109
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Keywords:

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

Supporting agencies:

This research was not funded

Abstract:

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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