Efroymson's approximation theorem for globally subanalytic functions

2019/05/14 by Anna Valette, Valette, Anna, Guillaume Valette +1
Mathematics · #14P10 #32B20 #41A30 #58A07 #Advanced Topics in Algebra #Advanced Topology and Set Theory #Algebraic Geometry (math.AG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1905.05703

openalex publication_date 2019/05/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Efroymson's approximation theorem asserts that if f is a C⁰ semialgebraic mapping on a C^∞ semialgebraic submanifold M of ℝⁿ and if ε:M→ ℝ is a positive continuous semialgebraic function then there is a C^∞ semialgebraic function g:M→ ℝ such that |f-g|

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