Geodesic
Interdependence of a theorem of Koebe and a theorem of Caratheodory
Matematičeskie zametki, Tome 10 (1971) no. 4, pp. 399-406.

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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. 
@article{MZM_1971_10_4_a3,
     author = {V. A. Zorich},
     title = {Interdependence of a theorem of {Koebe} and a theorem of {Caratheodory}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {399--406},
     publisher = {mathdoc},
     volume = {10},
     number = {4},
     year = {1971},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1971_10_4_a3/}
}
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V. A. Zorich. Interdependence of a theorem of Koebe and a theorem of Caratheodory. Matematičeskie zametki, Tome 10 (1971) no. 4, pp. 399-406. http://geodesic.mathdoc.fr/item/MZM_1971_10_4_a3/