Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Constructing universally small subsets of a given packing index in
  Polish groups   A subset of a Polish space $X$ is called universally small if it belongs to
each ccc $\sigma$-ideal with Borel base on $X$. Under CH in each uncountable
Abelian Polish group $G$ we construct a universally small subset $A_0\subset G$
such that $|A_0\cap gA_0|=\mathfrak c$ for each $g\in G$. For each cardinal
number $\kappa\in[5,\mathfrak c^+]$ the set $A_0$ contains a universally small
subset $A$ of $G$ with sharp packing index
$\pack^\sharp(A_\kappa)=\sup\{|\mathcal D|^+:\mathcal D\subset \{gA\}_{g\in G}$
is disjoint$\}$ equal to $\kappa$.

28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
27
The categories of this paper are: comp-gas
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
1
The categories of this paper are: cs