*Published Paper*

**Inserted:** 8 nov 2018

**Last Updated:** 8 nov 2018

**Journal:** Israel J. math.

**Year:** 2012

**Links:**
paper on arxiv

**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.