Runge families and inductive limits of Stein spaces
Annales de l'Institut Fourier, Volume 27 (1977) no. 3, pp. 117-127.

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.

Le problème général des réunions de Stein est résolu : étant donné une suite croissante des ouverts de Stein, on démontre que la réunion X est de Stein si et seulement si H 1 (X,O X ) est séparé.

@article{AIF_1977__27_3_117_0,
     author = {Markoe, Andrew},
     title = {Runge families and inductive limits of {Stein} spaces},
     journal = {Annales de l'Institut Fourier},
     pages = {117--127},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {27},
     number = {3},
     year = {1977},
     doi = {10.5802/aif.663},
     zbl = {0323.32014},
     mrnumber = {58 #28665},
     language = {en},
     url = {https://aif.centre-mersenne.org/articles/10.5802/aif.663/}
}
TY  - JOUR
AU  - Markoe, Andrew
TI  - Runge families and inductive limits of Stein spaces
JO  - Annales de l'Institut Fourier
PY  - 1977
SP  - 117
EP  - 127
VL  - 27
IS  - 3
PB  - Institut Fourier
PP  - Grenoble
UR  - https://aif.centre-mersenne.org/articles/10.5802/aif.663/
DO  - 10.5802/aif.663
LA  - en
ID  - AIF_1977__27_3_117_0
ER  - 
%0 Journal Article
%A Markoe, Andrew
%T Runge families and inductive limits of Stein spaces
%J Annales de l'Institut Fourier
%D 1977
%P 117-127
%V 27
%N 3
%I Institut Fourier
%C Grenoble
%U https://aif.centre-mersenne.org/articles/10.5802/aif.663/
%R 10.5802/aif.663
%G en
%F AIF_1977__27_3_117_0
Markoe, Andrew. Runge families and inductive limits of Stein spaces. Annales de l'Institut Fourier, Volume 27 (1977) no. 3, pp. 117-127. doi : 10.5802/aif.663. https://aif.centre-mersenne.org/articles/10.5802/aif.663/

[1] A. Andreotti and E. Vesentini, Carleman estimates for the Laplace-Beltrami equation on complex manifolds Publ. Math., No. 25, IHES, Paris (1965). | EuDML | Numdam | Zbl

[2] H. Behnke and P. Thullen, Theorie der Funktionen mehrerer komplexer Veränderlichen, Zweite erweiterte Auflage, Springer-Verlag, Berlin 1970. | Zbl

[3] J.E. Fornaess, An increasing sequence of Stein manifolds whose limit is not Stein, to appear. | Zbl

[4] H. Grauert, Charakterisierung der holomorph-vollständigen Raüme, Math. Ann., 129, (1955), 233-259. | EuDML | Zbl

[5] A. Grothendieck, éléments de géométrie algébrique, III (première Partie), Publ. Math. No. 11, IHES, Paris, 1961. | Numdam

[6] R. Gunning and H. Rossi, Analytic Functions of Several Complex Variables, Prentice Hall, Englewood Cliffs, N.J., 1965. | MR | Zbl

[7] H. Laufer, On Serre duality and envelopes of holomorphy, Trans. AMS, 128 (1967), 414-446. | MR | Zbl

[8] J.-P. Ramis and G. Ruget, Complexe dualisant et théorèmes de dualité en géométrie analytique complexe, Publ. Math., No. 38, IHES, Paris, 1971. | EuDML | Numdam | Zbl

[9] J.-P. Ramis, G. Ruget and J.-L. Verdier, Dualité relative en géométrie analytique complexe, Inv. Math., (1971). | EuDML | MR | Zbl

[10] A. Silva, Rungescherssatz and a condition for Steiness for the limit of an increasing sequence of Stein spaces.

[11] K. Stein, Überlagerungen holomorph-vollständiger komplexer Raüme, Arch. Math., 7 (1956), 354-361. | MR | Zbl

[12] J. Wermer, An example concerning polynomial convexity, Math. Ann., 139 (1959), 147-150. | MR | Zbl

[13] A. Hirschowitz, Pseudoconvexité au-dessus d'espaces plus ou moins homogènes, Inv. Math., 26 (1974), 303-322. | MR | Zbl

[14] H. Bhehnke and K. Stein, Konvergente Folgen von Reguläritätsbereichen und die meromorphe Konvexität, Math. Ann., 116 (1939), 204-216. | JFM | Zbl

[15] A. Markoe, Runge families and increasing unions of Stein spaces, research announcement, Bull. AMS, 82, No 5, (1976). | MR | Zbl

Cited by Sources: