Analysis reveals the properties of convex sets covering the unit ball in Banach spaces, indicating limitations for infinite dimensions.
Given a finite covering by closed convex sets of BX B X , the unit ball of an infinite-dimensional Banach space, we investigate whether there is a set of the covering that contains balls of radius close to 1 and (a) arbitrarily high finite dimension or (b) infinite dimension. In case (a) the answer is affirmative, but for the case (b) we just get radius close to 1/2 and finite codimension under much more restrictive hypotheses.
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M. Raja (2025) studied this question.
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