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On q -Runge pairs

Mihnea Colţoiu (2003)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

We show that the converse of the aproximation theorem of Andreotti and Grauert does not hold. More precisely we construct a 4 -complete open subset D 6 (which is an analytic complement in the unit ball) such that the restriction map H 3 ( 6 , ) H 3 ( D , ) has a dense image for every C o h ( 6 ) but the pair ( D , 6 ) is not a 4 -Runge pair.

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