On the products of Nash subvarieties by spheres
Alessandro Tancredi, Alberto Tognoli · Proceedings of the American Mathematical Society · 2005
We show that the product of any sphere by any compact connected component of a real algebraic variety is Nash isomorphic to a real algebraic variety, and we deduce such a result for some non-compact components, too. It follows also that the product of any sphere by any compact global Nash subvariety of $\mathbb R^n$ is Nash isomorphic to a real algebraic variety.