Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Normal tilings of a Banach space and its ball   We show some new results about tilings in Banach spaces. A tiling of a Banach
space $X$ is a covering by closed sets with non-empty interior so that they
have pairwise disjoint interiors. If moreover the tiles have inner radii
uniformly bounded from below, and outer radii uniformly bounded from above, we
say that the tiling is normal.
  In 2010 Preiss constructed a convex normal tiling of the separable Hilbert
space. For Banach spaces with Schauder basis we will show that Preiss' result
is still true with starshaped tiles instead of convex ones. Also, whenever $X$
is uniformly convex we give precise constructions of convex normal tilings of
the unit sphere, the unit ball or in general of any convex body.

18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
24
The categories of this paper are: dg-ga
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The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th
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The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
1
The categories of this paper are: cs