Approximation and the topology of rationally convex sets

Considering a mapping g holomorphic on a neighbourhood of a rationafly convex set K C C-n, and range into the complex projective space CPm, 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 CPm. We only need to ask that the second Cech cohomology group H-2 (K, Z) vanishes.