Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Steinhaus-type property for a boundary of a convex body   We show that if $U\subset\partial A$ is a neighbourhood of a point
$x_0\in\partial A$ of the boundary of a convex body $A$ then it has the
so-called Stainhaus-type property (the interior of $(U+U)$ is nonempty) if and
only if $x_0$ is not a point of flatness of the boundary~$\partial A$. This
implies that additive functions as well as mid-convex functions, bounded above
on~$U$, are continuous.

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
10
The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
1
The categories of this paper are: cs
23
The categories of this paper are: solv-int
20
The categories of this paper are: acc-phys
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th