Runge families and inductive limits of Stein spaces

Andrew Markoe

Annales de l'institut Fourier (1977)

  • Volume: 27, Issue: 3, page 117-127
  • ISSN: 0373-0956

Abstract

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The general Stein union problem is solved: given an increasing sequence of Stein open sets, it is shown that the union X is Stein if and only if H 1 ( X , O X ) is Hausdorff separated.

How to cite

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Markoe, Andrew. "Runge families and inductive limits of Stein spaces." Annales de l'institut Fourier 27.3 (1977): 117-127. <http://eudml.org/doc/74322>.

@article{Markoe1977,
abstract = {The general Stein union problem is solved: given an increasing sequence of Stein open sets, it is shown that the union $X$ is Stein if and only if $H^1(X,\{\bf O\}_X)$ is Hausdorff separated.},
author = {Markoe, Andrew},
journal = {Annales de l'institut Fourier},
language = {eng},
number = {3},
pages = {117-127},
publisher = {Association des Annales de l'Institut Fourier},
title = {Runge families and inductive limits of Stein spaces},
url = {http://eudml.org/doc/74322},
volume = {27},
year = {1977},
}

TY - JOUR
AU - Markoe, Andrew
TI - Runge families and inductive limits of Stein spaces
JO - Annales de l'institut Fourier
PY - 1977
PB - Association des Annales de l'Institut Fourier
VL - 27
IS - 3
SP - 117
EP - 127
AB - The general Stein union problem is solved: given an increasing sequence of Stein open sets, it is shown that the union $X$ is Stein if and only if $H^1(X,{\bf O}_X)$ is Hausdorff separated.
LA - eng
UR - http://eudml.org/doc/74322
ER -

References

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  1. [1] A. ANDREOTTI and E. VESENTINI, Carleman estimates for the Laplace-Beltrami equation on complex manifolds Publ. Math., No. 25, IHES, Paris (1965). Zbl0138.06604
  2. [2] H. BEHNKE and P. THULLEN, Theorie der Funktionen mehrerer komplexer Veränderlichen, Zweite erweiterte Auflage, Springer-Verlag, Berlin 1970. Zbl0204.39502
  3. [3] J.E. FORNAESS, An increasing sequence of Stein manifolds whose limit is not Stein, to appear. Zbl0334.32017
  4. [4] H. GRAUERT, Charakterisierung der holomorph-vollständigen Raüme, Math. Ann., 129, (1955), 233-259. Zbl0064.32603MR17,80d
  5. [5] A. GROTHENDIECK, éléments de géométrie algébrique, III (première Partie), Publ. Math. No. 11, IHES, Paris, 1961. 
  6. [6] R. GUNNING and H. ROSSI, Analytic Functions of Several Complex Variables, Prentice Hall, Englewood Cliffs, N.J., 1965. Zbl0141.08601MR31 #4927
  7. [7] H. LAUFER, On Serre duality and envelopes of holomorphy, Trans. AMS, 128 (1967), 414-446. Zbl0166.33903MR36 #5393
  8. [8] J.-P. RAMIS and G. RUGET, Complexe dualisant et théorèmes de dualité en géométrie analytique complexe, Publ. Math., No. 38, IHES, Paris, 1971. Zbl0206.25006
  9. [9] J.-P. RAMIS, G. RUGET and J.-L. VERDIER, Dualité relative en géométrie analytique complexe, Inv. Math., (1971). Zbl0218.14010MR46 #7553
  10. [10] A. SILVA, Rungescherssatz and a condition for Steiness for the limit of an increasing sequence of Stein spaces. 
  11. [11] K. STEIN, Überlagerungen holomorph-vollständiger komplexer Raüme, Arch. Math., 7 (1956), 354-361. Zbl0072.08002MR18,933a
  12. [12] J. WERMER, An example concerning polynomial convexity, Math. Ann., 139 (1959), 147-150. Zbl0094.28302MR22 #12238
  13. [13] A. HIRSCHOWITZ, Pseudoconvexité au-dessus d'espaces plus ou moins homogènes, Inv. Math., 26 (1974), 303-322. Zbl0275.32009MR50 #10323
  14. [14] H. BHEHNKE and K. STEIN, Konvergente Folgen von Reguläritätsbereichen und die meromorphe Konvexität, Math. Ann., 116 (1939), 204-216. Zbl0020.37803JFM64.0322.03
  15. [15] A. MARKOE, Runge families and increasing unions of Stein spaces, research announcement, Bull. AMS, 82, No 5, (1976). Zbl0334.32016MR54 #3026

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