Le problème général des réunions de Stein est résolu : étant donné une suite croissante des ouverts de Stein, on démontre que la réunion est de Stein si et seulement si est séparé.
The general Stein union problem is solved: given an increasing sequence of Stein open sets, it is shown that the union is Stein if and only if is Hausdorff separated.
@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},
volume = {27},
year = {1977},
pages = {117-127},
doi = {10.5802/aif.663},
mrnumber = {58 \#28665},
zbl = {0323.32014},
language = {en},
url = {http://dml.mathdoc.fr/item/AIF_1977__27_3_117_0}
}
Markoe, Andrew. Runge families and inductive limits of Stein spaces. Annales de l'Institut Fourier, Tome 27 (1977) pp. 117-127. doi : 10.5802/aif.663. http://gdmltest.u-ga.fr/item/AIF_1977__27_3_117_0/
[1] and , Carleman estimates for the Laplace-Beltrami equation on complex manifolds Publ. Math., No. 25, IHES, Paris (1965). | Numdam | Zbl 0138.06604
[2] and , Theorie der Funktionen mehrerer komplexer Veränderlichen, Zweite erweiterte Auflage, Springer-Verlag, Berlin 1970. | Zbl 0204.39502
[3] , An increasing sequence of Stein manifolds whose limit is not Stein, to appear. | Zbl 0334.32017
[4] , Charakterisierung der holomorph-vollständigen Raüme, Math. Ann., 129, (1955), 233-259. | Zbl 0064.32603
[5] , éléments de géométrie algébrique, III (première Partie), Publ. Math. No. 11, IHES, Paris, 1961. | Numdam
[6] and , Analytic Functions of Several Complex Variables, Prentice Hall, Englewood Cliffs, N.J., 1965. | MR 31 #4927 | Zbl 0141.08601
[7] , On Serre duality and envelopes of holomorphy, Trans. AMS, 128 (1967), 414-446. | MR 36 #5393 | Zbl 0166.33903
[8] and , Complexe dualisant et théorèmes de dualité en géométrie analytique complexe, Publ. Math., No. 38, IHES, Paris, 1971. | Numdam | Zbl 0206.25006
[9] , and , Dualité relative en géométrie analytique complexe, Inv. Math., (1971). | MR 46 #7553 | Zbl 0218.14010
[10] , Rungescherssatz and a condition for Steiness for the limit of an increasing sequence of Stein spaces.
[11] , Überlagerungen holomorph-vollständiger komplexer Raüme, Arch. Math., 7 (1956), 354-361. | MR 18,933a | Zbl 0072.08002
[12] , An example concerning polynomial convexity, Math. Ann., 139 (1959), 147-150. | MR 22 #12238 | Zbl 0094.28302
[13] , Pseudoconvexité au-dessus d'espaces plus ou moins homogènes, Inv. Math., 26 (1974), 303-322. | MR 50 #10323 | Zbl 0275.32009
[14] and , Konvergente Folgen von Reguläritätsbereichen und die meromorphe Konvexität, Math. Ann., 116 (1939), 204-216. | JFM 64.0322.03 | Zbl 0020.37803
[15] , Runge families and increasing unions of Stein spaces, research announcement, Bull. AMS, 82, No 5, (1976). | MR 54 #3026 | Zbl 0334.32016