### Impacto

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 |
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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 |

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Deposited On: | 17 Sep 2012 08:47 |

Last Modified: | 10 Feb 2016 16:03 |

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