Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Separately polynomial functions   It is known that if $f\colon {\mathbb R}^2 \to {\mathbb R}$ is a polynomial
in each variable, then $f$ is a polynomial. We present generalizations of this
fact, when ${\mathbb R}^2$ is replaced by $G\times H$, where $G$ and $H$ are
topological Abelian groups. We show, e.g., that the conclusion holds (with
generalized polynomials in place of polynomials) if $G$ is a connected Baire
space and $H$ has a dense subgroup of finite rank or, for continuous functions,
if $G$ and $H$ are connected Baire spaces. The condition of continuity can be
omitted if $G$ and $H$ are locally compact or complete metric spaces. We
present several examples showing that the results are not far from being
optimal.

28
The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
32
The categories of this paper are: atom-ph
13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph