Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On continuous self-maps and homeomorphisms of the Golomb space   The Golomb space $\mathbb N_\tau$ is the set $\mathbb N$ of positive integers
endowed with the topology $\tau$ generated by the base consisting of arithmetic
progressions $\{a+bn\}_{n=0}^\infty$ with coprime $a,b$. We prove that the
Golomb space $\mathbb N_\tau$ has continuum many continuous self-maps, contains
a countable disjoint family of infinite closed connected subsets, the set $\Pi$
of prime numbers is a dense metrizable subspace of $\mathbb N_\tau$, and each
homeomorphism $h$ of $\mathbb N_\tau$ has the following properties: $h(1)=1$,
$h(\Pi)=\Pi$ and $\Pi_{h(x)}=h(\Pi_x)$ for all $x\in\mathbb N$. Here by $\Pi_x$
we denote the set of prime divisors of $x$.

8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
26
The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga