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International Journal of Mathematics and Mathematical Sciences
Volume 27 (2001), Issue 1, Pages 39-44
http://dx.doi.org/10.1155/S0161171201005075

A note on nonfragmentability of Banach spaces

Department of Mathematics, Damghan College of Sciences, P.O. Box 364, Damghan 36715, Iran

Received 15 October 1999; Revised 4 May 2000

Copyright © 2001 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We use Kenderov-Moors characterization of fragmentability to show that if a compact Hausdorff space X with the tree-completeness property contains a disjoint sequences of clopen sets, then (C(X), weak) is not fragmented by any metric which is stronger than weak topology. In particular, C(X) does not admit any equivalent locally uniformly convex renorming.