Suárez Granero, AntonioJiménez Sevilla, María Del MarMoreno, José Pedro2023-06-202023-06-202002-06Suátrez Granero, A., Jiménez Sevilla, M. M., Moreno, J. P. «ON $\omega$-INDEPENDENCE AND THE KUNEN–SHELAH PROPERTY». Proceedings of the Edinburgh Mathematical Society, vol. 45, n.o 2, junio de 2002, pp. 391-95. DOI.org (Crossref), https://doi.org/10.1017/S0013091500001061.0013-091510.1017/S0013091500001061https://hdl.handle.net/20.500.14352/57522Supported in part by DGICYT grants PB 97-0240 and BMF2000-0609.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.engjournal articlehttps//doi.org/10.1017/S0013091500001061http://journals.cambridge.org/download.php?file=%2F45393_1096F213E7B4D681B4962188EFC5A6ED_journals__PEM_PEM2_45_02_http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=2720208restricted access515.1ω-independenceNon-separable Banach spacesKunen–Shelah propertyTopología1210 Topología