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arXiv · 1009.4681

On a question by Corson about point-finite coverings

Andrea Marchese·Clemente Zanco
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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.

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Andrea Marchese, Clemente Zanco. 2010-09-23. On a question by Corson about point-finite coverings. https://doi.org/10.1007/s11856-011-0126-1

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