An open mapping theorem for analytic multifunctions

Zbigniew Słodkowski

Studia Mathematica (1997)

  • Volume: 122, Issue: 2, page 117-122
  • ISSN: 0039-3223

Abstract

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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.

How to cite

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Słodkowski, Zbigniew. "An open mapping theorem for analytic multifunctions." Studia Mathematica 122.2 (1997): 117-122. <http://eudml.org/doc/216363>.

@article{Słodkowski1997,
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.},
author = {Słodkowski, Zbigniew},
journal = {Studia Mathematica},
keywords = {open mapping theorem; analytic multifunctions},
language = {eng},
number = {2},
pages = {117-122},
title = {An open mapping theorem for analytic multifunctions},
url = {http://eudml.org/doc/216363},
volume = {122},
year = {1997},
}

TY - JOUR
AU - Słodkowski, Zbigniew
TI - An open mapping theorem for analytic multifunctions
JO - Studia Mathematica
PY - 1997
VL - 122
IS - 2
SP - 117
EP - 122
AB - 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.
LA - eng
KW - open mapping theorem; analytic multifunctions
UR - http://eudml.org/doc/216363
ER -

References

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  1. [BaHa] L. Baribeau and S. Harbottle, Two new open mapping theorems for analytic multifunctions, Proc. Amer. Math. Soc. 115 (1992), 1009-1012. Zbl0755.30040
  2. [Ok] K. Oka, Note sur les familles de fonctions analytiques multiformes etc., J. Sci. Hiroshima Univ. 4 (1934), 93-98. Zbl60.0243.06
  3. [Ra1] T. J. Ransford, Open mapping, inversion and implicit function theorems for analytic multivalued functions, Proc. London Math. Soc. 49 (1984), 537-562. Zbl0526.46045
  4. [Ra2] T. J. Ransford, On the range of an analytic multivalued function, Pacific J. Math. 123 (1986), 421-439. Zbl0553.30034
  5. [Sł1] Z. Słodkowski, Analytic set-valued functions and spectra, Math. Ann. 256 (1981), 363-386. Zbl0452.46028
  6. [Sł2] Z. Słodkowski, Polynomial hulls in ℂ 2 and quasi-circles, Ann. Scuola Norm. Sup. Pisa (4) 16 (1989), 367-391. 

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