On the theorem converse to Jordan's curve theorem

Details On the theorem converse to Jordan's curve theorem On the theorem converse to Jordan's curve theorem

2000-09-16

arxiv.org/abs/math/0009164v1

Mathematics

Geometric Topology

Scientific paper

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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