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Kadec norms and Borel sets in a Banach space

100%

Raja M.

Studia Mathematica

1999

tom 136

nr 1

1-16

We introduce a property for a couple of topologies that allows us to give simple proofs of some classic results about Borel sets in Banach spaces by Edgar, Schachermayer and Talagrand as well as some new results. We characterize the existence of Kadec type renormings in the spirit of the new results for LUR spaces by Moltó, Orihuela and Troyanski.

On having a countable cover by sets of small local diameter

100%

Ribarska N. K.

Studia Mathematica

2000

tom 140

nr 2

99-116

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.

Ograniczanie wyników

2 Studia Mathematica

1 Raja M.

1 Ribarska N. K.

1 2000

1 1999

Wyniki wyszukiwania

Kadec norms and Borel sets in a Banach space

On having a countable cover by sets of small local diameter