Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stability of systems of general functional equations in the compact-open
  topology   We introduce a fairly general concept of functional equation for $k$-tuples
of functions $f_1,\dots,f_k\colon X \to Y$ between arbitrary sets. The
homomorphy equations for mappings between groups and other algebraic systems,
as well as various types of functional equations and recursion formulas
occurring in mathematical analysis or combinatorics, respectively, become
special cases (of systems) of such equations. Assuming that $X$ is a locally
compact and $Y$ is a completely regular topological space, we show that systems
of such functional equations, with parameters satisfying rather a modest
continuity condition, are stable in the following intuitive sense: Every
$k$-tuple of ``sufficiently continuous,'' ``reasonably bounded'' functions $X
\to Y$ satisfying the given system with a ``sufficient precision'' on a ``big
enough'' compact set is already ``arbitrarily close'' on an ``arbitrarily big''
compact set to a $k$-tuple of continuous functions solving the system. The
result is derived as a consequence of certain intuitively appealing
``almost-near'' principle using the relation of infinitesimal nearness
formulated in terms of nonstandard analysis.

11
The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org
27
The categories of this paper are: comp-gas
1
The categories of this paper are: cs
34
The categories of this paper are: chem-ph
28
The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
14
The categories of this paper are: math-ph
24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys