Complutense University Library

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

[img] PDF
Restringido a Repository staff only hasta 31 December 2020.


Official URL:


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

C. Finet and G. Godefroy, Biorthogonal systems and big quotient spaces, Contemp. Math. 85 (1989), 87–110.

D. H. Fremlin and A. Sersouri, On ω-independence in separable Banach spaces, Q. J. Math. 39 (1988), 323–331.

A. S. Granero, M. Jiménez-Sevilla and J. P. Moreno, Convex sets in Banach spaces and a problem of Rolewicz, Studia Math. 129 (1998), 19–29.

M. Jiménez-Sevilla and J. P. Moreno, Renorming Banach spaces with the Mazur intersection property, J. Funct. Analysis 144 (1997), 486–504.

N. J. Kalton, Independence in separable Banach spaces, Contemp. Math. 85 (1989), 319–323.

S. Negrepontis, Banach spaces and topology, in Handbook of set-theoretic topology, pp. 1045–1142 (North-Holland, Amsterdam, 1984).

R. R. Phelps, Convex functions, monotone operators and differentiability, 2nd edn, Lecture Notes in Mathematics, no. 1364 (Springer, 1993).

A. Sersouri, ω-independence in nonseparable Banach spaces, Contemp. Math. 85 (1989), 509–512.

S. Shelah, A Banach space with few operators, Israel J. Math. 30 (1978), 181–191.

S. Shelah, Uncountable constructions for B.A., e.c. groups and Banach spaces, Israel J. Math. 51 (1985), 273–297.

Deposited On:17 Sep 2012 08:47
Last Modified:10 Feb 2016 16:03

Repository Staff Only: item control page