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Interdependence of a theorem of Koebe and a theorem of caratheodory

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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.

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Authors and Affiliations

  1. M. V. Lomonosov Moscow State University, USSR

    V. A. Zorich

Authors
  1. V. A. Zorich
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Translated from Matematicheskie Zametki, Vol. 10, No. 4, 399–406, October, 1971.

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Zorich, V.A. Interdependence of a theorem of Koebe and a theorem of caratheodory. Mathematical Notes of the Academy of Sciences of the USSR 10, 662–666 (1971). https://doi.org/10.1007/BF01106461

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  • DOI: https://doi.org/10.1007/BF01106461

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