Proceedings of the American Mathematical Society

Author(s): B. Cascales; I. Namioka; G. Vera
Journal: Proc. Amer. Math. Soc. 128 (2000), 3301-3309.
MSC (2000): Primary 46A50, 46B22; Secondary 54C35
Posted: April 28, 2000
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Abstract: Let

be a compact Hausdorff space and

the space of continuous real functions on

. In this paper we prove that any $t_{p}(K)$ -Lindelöf subset of

which is compact for the topology $t_{p}(D)$ of pointwise convergence on a dense subset $D\subset K$ is norm fragmented; i.e., each non-empty subset of it contains a non-empty $t_{p}(D)$ -relatively open subset of small supremum norm diameter. Several applications are given.

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Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 46A50, 46B22, 54C35

B. Cascales
Affiliation: Departamento de Matemáticas, Facultad de Matemáticas, Universidad de Murcia, 30.100 Espinardo, Murcia, Spain
Email: beca@fcu.um.es

I. Namioka
Affiliation: Department of Mathematics, Box 354350, University of Washington, Seattle, Washington 98195--4350
Email: namioka@math.washington.edu

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