Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Galois connection related to restrictions of continuous real functions   Given a family of continuous real functions $\mathcal{G}$, let
$R_\mathcal{G}$ be a binary relation defined as follows: a continuous function
$f\colon\mathbb{R}\to\mathbb{R}$ is in the relation with a closed set
$E\subseteq\mathbb{R}$ if and only if there exists $g\in\mathcal{G}$ such that
$f\upharpoonright E = g\upharpoonright E$. We consider a Galois connection
between families of continuous functions and hereditary families of closed sets
of reals naturally associated to $R_\mathcal{G}$. We study complete lattices
determined by this connection and prove several results showing the dependence
of the properties of these lattices on the properties of $\mathcal{G}$. In some
special cases we obtain exact description of these lattices.

6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
24
The categories of this paper are: dg-ga
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
17
The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
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The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys