Approximation on Nash sets with monomial singularities



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Baro González, Elías and Fernando Galván, José Francisco and Ruiz Sancho, Jesús María (2014) Approximation on Nash sets with monomial singularities. Advances in mathematics (262). pp. 59-114. ISSN 0001-8708

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This paper is devoted to the approximation of differentiable semialgebraic functions by Nash functions. Approximation by Nash functions is known for semialgebraic functions defined on an affine Nash manifold M, and here we extend it to functions defined on Nash subsets X of M whose singularities are monomial. To that end we discuss first "finiteness" and "weak normality" for such sets X. Namely, we prove that (i) X is the union of finitely many open subsets, each Nash diffeomorphic to a finite union of coordinate linear varieties of an affine space and (ii) every function on X which is Nash on every irreducible component of X extends to a Nash function on M. Then we can obtain approximation for semialgebraic functions and even for certain semialgebraic maps on Nash sets with monomial singularities. As a nice consequence we show that m-dimensional affine Nash manifolds with divisorial corners which are class k semialgebraically diffeomorphic, for k>m^2, are also Nash diffeomorphic.

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Corrigendum to “Approximation on Nash sets with monomial singularities” [Adv. Math. 262 (2014) 59–114]

Uncontrolled Keywords:Semialgebraic; Nash; Approximation; Extension; Monomial singularity; Manifold with corners
Subjects:Sciences > Mathematics
ID Code:28998
Deposited On:04 Mar 2015 10:49
Last Modified:12 Dec 2018 15:12

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