Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Continuous rational maps into spheres   Let X be a compact nonsingular real algebraic variety. We prove that if a
continuous map from X into the unit p-sphere is homotopic to a continuous
rational map, then, under certain assumptions, it can be approximated in the
compact-open topology by continuous rational maps. As a byproduct, we also
obtain some results on approximation of smooth submanifolds by nonsingular
subvarieties.

30
The categories of this paper are: q-alg
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph
13
The categories of this paper are: quant-ph
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
26
The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys
1
The categories of this paper are: cs