On having a countable cover by sets of small local diameter
Volume 140 / 2000
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.
