This article is cited 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.

UDC: 517.54

Received: 20.11.1970

 English version: Mathematical Notes, 1971, 10:4, 662–666

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