Asymptotic structures of cardinals

Asymptotic structures of cardinals

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 equiv...

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Bibliographic Details
Main Authors: Oleksandr Petrenko, Igor V. Protasov, Sergii Slobodianiuk
Format: Article
Language:English
Published: Universitat Politècnica de València 2014-07-01
Series:Applied General Topology
Subjects:
cardinal balleans
coarse equivalence
metrizability
cellularity
cardinal invariants
ultrafilter.
Online Access:http://polipapers.upv.es/index.php/AGT/article/view/3109
Description
Summary: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.
ISSN:1576-9402
1989-4147

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