RT Journal Article
T1 Approximation on Nash sets with monomial singularities
A1 Baro González, Elías
A1 Fernando Galván, José Francisco
A1 Ruiz Sancho, Jesús María
AB 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.
PB Elsevier
SN 0001-8708
YR 2014
FD 2014-09
LK https://hdl.handle.net/20.500.14352/33838
UL https://hdl.handle.net/20.500.14352/33838
LA eng
NO Corrigendum to “Approximation on Nash sets with monomial singularities” [Adv. Math. 262 (2014) 59–114]
NO Spanish GAAR
DS Docta Complutense
RD 30 abr 2024