Abstract

KENNEDY, JUDY. A really topological treatment of some aspects of Carathéodory’s theory of prime ends. Integración - UIS [online]. 2023, vol.41, n.1, pp.57-67.  Epub Oct 04, 2023. ISSN 0120-419X.  https://doi.org/10.18273/revint.v41n1-2023004.

A homeomorphism approximation technique is applied to give (1) proofs of some theorems of C. Carathéodory, and (2) a proof of a theorem of N. Rutt. The proofs use only tools from general topology (and are new in that respect), and a generalization of a theorem of Carathéodory is obtained.

Keywords : Carathéodory’s Theory of Prime Ends; homeomorphism approximation; homeomorphism construction; indecomposable continuum; Schoenflies Theorem; confluent mapping; monotone mapping.

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