Asymptotic structures of cardinals
type: Item
instance of: scholarly article
title: Asymptotic structures of cardinals
zbMATH Open document ID: 1304.54009
author: Oleksandr Petrenko
author: Sergii Slobodianiuk
author: Igor V. Protasov
published in: Applied General Topology
publication date: 2014-10-09T00:00:00Z
full work available at URL: https://arxiv.org/abs/1310.1828
Mathematics Subject Classification ID: 54A25
Mathematics Subject Classification ID: 05A18
Mathematics Subject Classification ID: 54E35
zbMATH DE Number: 6353143
zbMATH Keywords: ball structure
zbMATH Keywords: cardinal balleans
zbMATH Keywords: coarse equivalence
zbMATH Keywords: metrisability
zbMATH Keywords: cellularity
zbMATH Keywords: cardinal invariants
zbMATH Keywords: ultrafilter
MaRDI profile type: Publication
OpenAlex ID: W2045171210
arXiv ID: 1310.1828
cites work: Spread of balleans
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cites work: Thin ultrafilters
cites work: Resolvability of ball structures
cites work: Cellularity and density of balleans
cites work: The combinatorial derivation.
cites work: Q3392760
cites work: Q3518445
cites work: Q4437801
cites work: Homogeneity problems in the theory of Cech compactifications
DOI: 10.4995/AGT.2014.3109
review text: A ballean is a triple \((X,P,B)\), where \(X\) and \(P\) are non-empty sets and \(B:X\times P\to 2^X\) such that \(x\in B(x,\alpha)\), for any \(\alpha\in P\) there are \(\alpha',\alpha''\in P\) such that \(B(x,\alpha)\subset B^*(x,\alpha')=\{y\in X\mid x\in B(y,\alpha')\}\) and \(B^*(x,\alpha)\subset B(x,\alpha'')\), for any \(\alpha,\beta\in P\) there is \(\gamma\in P\) such that \(B(B(x,\alpha),\beta)\subset B(x,\gamma)\) for each \(x\in X\) and for each \(x,y\in X\) there is \(\alpha\in P\) with \(y\in B(x,\alpha)\). The ballean \((\kappa,\kappa, \overset {B}\leftrightarrow)\), for a given cardinal \(\kappa\), where \(\overset{B}{\leftrightarrow}(x,\alpha)=\{y\in\kappa\mid x\in[y,y+\alpha] \text{ or } y\in[x,x+\alpha]\}\) is the main object of investigation, particularly when it is equivalent to a metric ballean and some relevant cardinal invariants.
reviewed by: David B. Gauld
description: scientific article; zbMATH DE number 6353143