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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 open maps of Borel sets

75%

Ostrovsky A. V.

Fundamenta Mathematicae

1994-1995

tom 146

nr 3

203-213

We answer in the affirmative [Th. 3 or Corollary 1] the question of L. V. Keldysh [5, p. 648]: can every Borel set X lying in the space of irrational numbers ℙ not $G_δ · F_σ$ and of the second category in itself be mapped onto an arbitrary analytic set Y ⊂ ℙ of the second category in itself by an open map? Note that under a space of the second category in itself Keldysh understood a Baire space. The answer to the question as stated is negative if X is Baire but Y is not Baire.

Ograniczanie wyników

1 Fundamenta Mathematicae

1 Studia Mathematica

1 Ostrovsky A. V.

1 Raja M.

1 1999

1 1995

Wyniki wyszukiwania

Kadec norms and Borel sets in a Banach space

On open maps of Borel sets