Calculus of Variations and Geometric Measure Theory

A. Marchese - C. Zanco

On a question by Corson about point-finite coverings

created by marchese on 08 Nov 2018


Published Paper

Inserted: 8 nov 2018
Last Updated: 8 nov 2018

Journal: Israel J. math.
Year: 2012
Links: paper on arxiv


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.