Approximation and the topology of rationally convex sets

Eduardo S. Zeron

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Approximation and the topology of rationally convex sets

Eduardo S. Zeron

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Abstract

Considering a mapping g holomorphic on a neighbourhood of a rationally convex set K in $C^n$, 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 $C^n$ into $P^m$. We only need to ask that the second Cech cohomology group $\check{H}^2(K)$ vanishes.

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Eduardo S. Zeron. 2006-07-20. Approximation and the topology of rationally convex sets. https://arxiv.org/abs/math/0607500

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