On a question by Corson about point-finite coverings
Functional Analysis
2014-08-14 v1
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.
Keywords
Cite
@article{arxiv.1009.4681,
title = {On a question by Corson about point-finite coverings},
author = {Andrea Marchese and Clemente Zanco},
journal= {arXiv preprint arXiv:1009.4681},
year = {2014}
}
Comments
to appear on Israel J. Math