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
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