Geodesic
On having a countable cover by sets of small local diameter
Studia Mathematica, Tome 140 (2000) no. 2, pp. 99-116
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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.
DOI : 10.4064/sm-140-2-99-116
Keywords: countable cover by sets of small local diameter, fragmentability, Kadec renorming 
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Nadezhda K. Ribarska. On having a countable cover by sets of small local diameter. Studia Mathematica, Tome 140 (2000) no. 2, pp. 99-116. doi: 10.4064/sm-140-2-99-116

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