This is an announcement for the paper "On a question by Corson about point-finite coverings" by Andrea Marchese and Clemente Zanco.

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 nonempty 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 nonempty interior (tiles) such that the interiors are pairwise disjoint and no point of X belongs to more than two tiles.

Archive classification: math.FA

Remarks: to appear on Israel J. Math

Submitted from: marchese@mail.dm.unipi.it

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1009.4681

or

http://arXiv.org/abs/1009.4681