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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Behnke-Stein theorem for analytic spaces


Author: Alessandro Silva
Journal: Trans. Amer. Math. Soc. 199 (1974), 317-326
MSC: Primary 32E15
DOI: https://doi.org/10.1090/S0002-9947-1974-0367286-2
Addendum: Trans. Amer. Math. Soc. 212 (1975), 417-418.
MathSciNet review: 0367286
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Abstract: The notion of $ q$-Runge pair is extended to reduced complex analytic spaces. A necessary and sufficient condition for a pair of $ n$-dimensional analytic spaces to be an $ n$-Runge pair is proved and it is shown that this result extends a Behnke-Stein theorem when $ n = 1$. A topological property of $ q$-Runge pairs of spaces is also proved.


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DOI: https://doi.org/10.1090/S0002-9947-1974-0367286-2
Keywords: $ q$-Runge pairs, cohomologically $ q$-complete analytic spaces, Hausdorff cohomology, dualizing complex and derived functors
Article copyright: © Copyright 1974 American Mathematical Society