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This article is cited in 1 scientific paper (total in 1 paper)
Interdependence of a theorem of Koebe and a theorem of Caratheodory
V. A. Zorich M. V. Lomonosov Moscow State University
Abstract:
We determine the widest class of topological mappings for which a correspondence of boundaries is describable in terms of prime ends in the sense of Caratheodory. Relying on a concept of relative distance, we explain why the class so determined is the widest possible, and using a characteristic property of mappings of this class we prove a generalized theorem of Koebe on correspondence of accessible points and we establish its logical equivalence to a fundamental theorem of the Caratheodory theory.
Received: 20.11.1970
Citation:
V. A. Zorich, “Interdependence of a theorem of Koebe and a theorem of Caratheodory”, Mat. Zametki, 10:4 (1971), 399–406; Math. Notes, 10:4 (1971), 662–666
Linking options:
https://www.mathnet.ru/eng/mzm9728 https://www.mathnet.ru/eng/mzm/v10/i4/p399
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Abstract page: | 257 | Full-text PDF : | 110 | First page: | 1 |
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