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Approximation and the Topology of Rationally Convex Sets

Published:2006-12-01
Printed: Dec 2006
• E. S. Zeron
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Abstract

Considering a mapping $g$ holomorphic on a neighbourhood of a rationally convex set $K\subset\cc^n$, and range into the complex projective space $\cc\pp^m$, the main objective of this paper is to show that we can uniformly approximate $g$ on $K$ by rational mappings defined from $\cc^n$ into $\cc\pp^m$. We only need to ask that the second \v{C}ech cohomology group $\check{H}^2(K,\zz)$ vanishes.
 Keywords: Rationally convex, cohomology, homotopy
 MSC Classifications: 32E30 - Holomorphic and polynomial approximation, Runge pairs, interpolation 32Q55 - Topological aspects of complex manifolds