On the theorem converse to Jordan's curve theorem

Eugene Polulyakh

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arXiv · math/0009164

On the theorem converse to Jordan's curve theorem

Eugene Polulyakh

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Abstract

Theorem converse to Jordan's curve theorem says that {\it if a compact set $K$ has two complementary domains in $R^{2}$, 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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Eugene Polulyakh. 2000-09-16. On the theorem converse to Jordan's curve theorem. https://arxiv.org/abs/math/0009164

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