Approximation and the topology of rationally convex sets

2006/07/20 by Eduardo S. Zeron, Zeron, Eduardo S.
Computer Science · Mathematics · #32E30 or 32Q55 #Advanced Banach Space Theory #Algebraic Topology (math.AT) #Complex Variables (math.CV) #FOS: Mathematics #Optimization and Variational Analysis #math.AT #math.CV #msc:32E30 #msc:32Q55

paper · pdf · doi:10.48550/arxiv.math/0607500

9 pages

arxiv created 2006/07/20 · openalex publication_date 2006/07/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Considering a mapping g holomorphic on a neighbourhood of a rationally convex set K in Cⁿ, and range into the complex projective space P^m, the main objective of this paper is to show that we can uniformly approximate g on K by rational mappings defined from Cⁿ into P^m. We only need to ask that the second Cech cohomology group \checkH²(K) vanishes.

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• Approximation and homotopy in regulous geometry