Algebraic approximation preserving dimension

2014/09/23 by Massimo Ferrarotti, Ferrarotti, Massimo, Elisabetta Fortuna +3
Decision Sciences · Mathematics · #14P15 #Advanced Optimization Algorithms Research #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #FOS: Mathematics #Fuzzy and Soft Set Theory

paper · pdf · doi:10.48550/arxiv.1409.6451

openalex publication_date 2014/09/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that each semialgebraic subset of \Rⁿ of positive codimension can be locally approximated of any order by means of an algebraic set of the same dimension. As a consequence of previous results, algebraic approximation preserving dimension holds also for semianalytic sets.

Related

• Local algebraic approximation of semianalytic sets
• Semidefinite approximations of projections and polynomial images of semialgebraic sets
• Efroymson's approximation theorem for globally subanalytic functions
• Approximation of analytic sets with proper projection by algebraic sets
• Exact Approximation In The Field Of Formal Series