Instytut Matematyczny Polskiej Akademii Nauk / Institute of Mathematics / Publishing house / Journals and Serials / Studia Mathematica / All issues

Abstract

The paper gives sufficient conditions for projections of certain pseudoconcave sets to be open. More specifically, it is shown that the range of an analytic set-valued function whose values are simply connected planar continua is open, provided there does not exist a point which belongs to boundaries of all the fibers. The main tool is a theorem on existence of analytic discs in certain polynomially convex hulls, obtained earlier by the author.