Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Small Sets containing any Pattern   Given any dimension function $h$, we construct a perfect set $E \subseteq
\mathbb{R}$ of zero $h$-Hausdorff measure, that contains any finite polynomial
pattern.
  This is achieved as a special case of a more general construction in which we
have a family of functions $\mathcal{F}$ that satisfy certain conditions and we
construct a perfect set $E$ in $\mathbb{R}^N$, of $h$-Hausdorff measure zero,
such that for any finite set $\{ f_1,\ldots,f_n\}\subseteq \mathcal{F}$, $E$
satisfies that $\bigcap_{i=1}^n f^{-1}_i(E)\neq\emptyset$.
  We also obtain an analogous result for the images of functions. Additionally
we prove some related results for countable (not necessarily finite)
intersections, obtaining, instead of a perfect set, an $\mathcal{F}_{\sigma}$
set without isolated points.

13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
12
The categories of this paper are: nucl-th
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
19
The categories of this paper are: eess