International Journal of Mathematics and Mathematical Sciences
Volume 27 (2001), Issue 1, Pages 39-44
doi: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 S. Alireza Kamel Mirmostafaee. 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.