Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On minimal non-potentially closed subsets of the plane   We study the Borel subsets of the plane that can be made closed by refining
the Polish topology on the real line. These sets are called potentially closed.
We first compare Borel subsets of the plane using products of continuous
functions. We show the existence of a perfect antichain made of minimal sets
among non-potentially closed sets. We apply this result to graphs, quasi-orders
and partial orders. We also give a non-potentially closed set minimum for
another notion of comparison. Finally, we show that we cannot have injectivity
in the Kechris-Solecki-Todorcevic dichotomy about analytic graphs.

1
The categories of this paper are: cs
15
The categories of this paper are: nucl-ex
20
The categories of this paper are: acc-phys
23
The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
12
The categories of this paper are: nucl-th
11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio
19
The categories of this paper are: eess
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom