A really topological treatment of some aspects of Carathéodory’s theory of prime ends

Abstract

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