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Displaying similar documents to “Selection theorems for partitions of Polish spaces”

On having a countable cover by sets of small local diameter

Nadezhda Ribarska (2000)

Studia Mathematica

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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.