On a question by Corson about point-finite coverings

Details On a question by Corson about point-finite coverings On a question by Corson about point-finite coverings

2010-09-23

arxiv.org/abs/1009.4681v1

Mathematics

Functional Analysis

to appear on Israel J. Math

Scientific paper

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.

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