Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Star-finite coverings of Banach spaces   We study star-finite coverings of infinite-dimensional normed spaces. A
family of sets is called star-finite if each of its members intersects only
finitely many other members of the family. It follows by our results that an
LUR or a uniformly Fr\'echet smooth infinite-dimensional Banach space does not
admit star-finite coverings by closed balls. On the other hand, we present a
quite involved construction proving existence of a star-finite covering of
$c_0(\Gamma)$ by Fr\'echet smooth centrally symmetric bounded convex bodies. A
similar but simpler construction shows that every normed space of countable
dimension (and hence incomplete) has a star-finite covering by closed balls.

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The categories of this paper are: physics
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The categories of this paper are: q-alg
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The categories of this paper are: alg-geom
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The categories of this paper are: bayes-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-lat
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The categories of this paper are: stat
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The categories of this paper are: nucl-th
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The categories of this paper are: funct-an
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The categories of this paper are: plasm-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: astro-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-bio
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The categories of this paper are: chem-ph