A well known result due to H. Corson states that, for any covering $\tau$ by closed bounded convex subsets of any Banach space $X$ containing an infinite-dimensional reflexive subspace, there exists a compact subset $C$ of $X$ that meets infinitely many members of $\tau$. We strengthen this result proving that, even under the weaker assumption that $X$ contains an infinite-dimensional separable dual space, a (algebraically) finite-dimensional compact set $C$ with that property can always be found.

Finitely locally finite coverings of Banach spaces / V.P. Fonf, C. Zanco. - In: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. - ISSN 0022-247X. - 350:2(2009), pp. 640-650.

### Finitely locally finite coverings of Banach spaces

#### Abstract

A well known result due to H. Corson states that, for any covering $\tau$ by closed bounded convex subsets of any Banach space $X$ containing an infinite-dimensional reflexive subspace, there exists a compact subset $C$ of $X$ that meets infinitely many members of $\tau$. We strengthen this result proving that, even under the weaker assumption that $X$ contains an infinite-dimensional separable dual space, a (algebraically) finite-dimensional compact set $C$ with that property can always be found.
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Covering; Finitely locally finite covering; Locally finite covering
Settore MAT/05 - Analisi Matematica
http://hdl.handle.net/2434/38182
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/61610
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