On the theorem converse to Jordan's curve theorem

2000/09/16 by Eugene Polulyakh, Polulyakh, Eugene
Mathematics · #14E35 #57M50 #57N35 #Advanced Banach Space Theory #Advanced Topology and Set Theory #FOS: Mathematics #General Topology (math.GN) #Geometric Topology (math.GT) #Mathematics and Applications #math.GN #math.GT #msc:14E35 #msc:57M50 #msc:57N35

paper · pdf · doi:10.48550/arxiv.math/0009164

arxiv created 2000/09/16 · openalex publication_date 2000/09/16 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Theorem converse to Jordan's curve theorem says that \it if a compact set K has two complementary domains in R², from each of which it is at every point accessible, it is a simple closed curve. We show that the requirement of this theorem that \it all points of K were accessible from \it both complementary domains is surplus and prove one generalization of this theorem.

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