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.
@article{bwmeta1.element.bwnjournal-article-smv122i2p117bwm,
author = {Zbigniew S\l odkowski},
title = {An open mapping theorem for analytic multifunctions},
journal = {Studia Mathematica},
volume = {122},
year = {1997},
pages = {117-122},
zbl = {0873.32012},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv122i2p117bwm}
}
Słodkowski, Zbigniew. An open mapping theorem for analytic multifunctions. Studia Mathematica, Tome 122 (1997) pp. 117-122. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv122i2p117bwm/
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