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ArticleOriginal scientific text

Title

On having a countable cover by sets of small local diameter

Authors 1

Affiliations

  1. Department of Mathematics and Informatics, University of Sofia, J. Bourchier boul. 5a, 1164 Sofia, Bulgaria

Abstract

A characterization of topological spaces admitting a countable cover by sets of small local diameter close in spirit to known characterizations of fragmentability is obtained. It is proved that if X and Y are Hausdorff compacta such that C(X) has an equivalent p-Kadec norm and Cp(Y) has a countable cover by sets of small local norm diameter, then Cp(X×Y) has a countable cover by sets of small local norm diameter as well.

Keywords

ENG
countable cover by sets of small local diameter, fragmentability, Kadec renorming

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Studia Mathematica
2000/140/2
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Pages:
99-116
Main language of publication
English
Received
1998-12-22
Accepted
2000-01-13
Published
2000
Exact and natural sciences