Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dimensions, Whitney covers, and tubular neighborhoods   Working in doubling metric spaces, we examine the connections between
different dimensions, Whitney covers, and geometrical properties of tubular
neighborhoods. In the Euclidean space, we relate these concepts to the behavior
of the surface area of the boundaries of parallel sets. In particular, we give
characterizations for the Minkowski and the spherical dimensions by means of
the Whitney ball count.

25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org
13
The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
9
The categories of this paper are: nlin