We answer in the affirmative the following question raised by H. H. Corson in 1961: "Is it possible to cover every Banach space X by bounded convex sets with non-empty interior in such a way that no point of X belongs to infinitely many of them?"Actually, we show the way to produce in every Banach space X a bounded convex tiling of order 2, i. e., a covering of X by bounded convex closed sets with non-empty interior (tiles) such that the interiors are pairwise disjoint and no point of X belongs to more than two tiles. © 2011 Hebrew University Magnes Press.
On a question by Corson about point-finite coverings / Marchese, A.; Zanco, C.. - In: ISRAEL JOURNAL OF MATHEMATICS. - ISSN 0021-2172. - 189:1(2012), pp. 55-63. [10.1007/s11856-011-0126-1]
On a question by Corson about point-finite coverings
Marchese A.;
2012-01-01
Abstract
We answer in the affirmative the following question raised by H. H. Corson in 1961: "Is it possible to cover every Banach space X by bounded convex sets with non-empty interior in such a way that no point of X belongs to infinitely many of them?"Actually, we show the way to produce in every Banach space X a bounded convex tiling of order 2, i. e., a covering of X by bounded convex closed sets with non-empty interior (tiles) such that the interiors are pairwise disjoint and no point of X belongs to more than two tiles. © 2011 Hebrew University Magnes Press.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione
