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On ω-independence and the Kunen-Shelah property

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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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
Additional Information: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
References:

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Deposited On:17 Sep 2012 08:47
Last Modified:07 Feb 2014 09:28

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