On the products of Nash subvarieties by spheres

Tancredi, Alessandro; Tognoli, Alberto

doi:10.1090/S0002-9939-05-08246-8

On the products of Nash subvarieties by spheres
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by Alessandro Tancredi and Alberto Tognoli PDF

Proc. Amer. Math. Soc. 134 (2006), 983-987 Request permission

Abstract:

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.

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