Recently continuous rational maps between real algebraic varieties have
attracted the attention of several researchers. In this paper we continue the
investigation of approximation properties of continuous rational maps with
values in spheres. We propose a conjecture concerning such maps and show that
it follows from certain classical conjectures involving transformation of
compact smooth submanifolds of nonsingular real algebraic varieties onto
subvarieties. Furthermore, we prove our conjecture in a special case and obtain
several related results.Comment: arXiv admin note: text overlap with arXiv:1403.512
