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On ω-independence and the Kunen-Shelah property

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Jiménez Sevilla, María del Mar and Granero, A. S. and Moreno, José Pedro (2002) On ω-independence and the Kunen-Shelah property. Proceedings of the Edinburgh Mathematical Society, 45 (2). pp. 391-395. ISSN 0013-0915

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Official URL: http://journals.cambridge.org/download.php?file=%2F45393_1096F213E7B4D681B4962188EFC5A6ED_journals__PEM_PEM2_45_02_http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=2720208




Abstract

We prove that spaces with an uncountable omega-independent family fail the Kunen-Shelah property. Actually, if {x(i)}(iis an element ofI) is an uncountable w-independent family, there exists an uncountable subset J.C I such that x(j) is not an element of (conv) over bar({x(i)}(iis an element ofj/{j}) for every j is an element of J. This improves a previous result due to Sersouri, namely that every uncountable omega-independent family contains a convex right-separated subfamily.


Item Type:Article
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Supported in part by DGICYT grants PB 97-0240 and BMF2000-0609.

Uncontrolled Keywords:ω-independence; non-separable Banach spaces; Kunen–Shelah property
Subjects:Sciences > Mathematics > Topology
ID Code:16386
Deposited On:17 Sep 2012 08:47
Last Modified:27 Jul 2018 07:42

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