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Approximation and the Topology of Rationally Convex Sets
Published online by Cambridge University Press: 20 November 2018
Abstract
Considering a mapping $g$ holomorphic on a neighbourhood of a rationally convex set $K\subset {{\mathbb{C}}^{n}}$, and range into the complex projective space $\mathbb{C}{{\mathbb{P}}^{m}}$, the main objective of this paper is to show that we can uniformly approximate $g$ on $K$ by rational mappings defined from ${{\mathbb{C}}^{n}}$ into $\mathbb{C}{{\mathbb{P}}^{m}}$. We only need to ask that the second Čech cohomology group ${{\overset{\scriptscriptstyle\smile}{H}}^{2}}\left( K,\mathbb{Z} \right)$ vanishes.
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- Copyright © Canadian Mathematical Society 2006
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