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 Rationally convex, cohomology, homotopy

MSC Classifications:

32E30, 32Q55 show english descriptions Holomorphic and polynomial approximation, Runge pairs, interpolation
Topological aspects of complex manifolds 32E30 - Holomorphic and polynomial approximation, Runge pairs, interpolation
32Q55 - Topological aspects of complex manifolds

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