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On having a countable cover by sets of small local diameter

Volume 140 / 2000

Nadezhda K. Ribarska Studia Mathematica 140 (2000), 99-116 DOI: 10.4064/sm-140-2-99-116

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 $C_p(Y)$ has a countable cover by sets of small local norm diameter, then $C_p(X×Y)$ has a countable cover by sets of small local norm diameter as well.

Authors

  • Nadezhda K. Ribarska

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