On the theorem converse to Jordan's curve theorem

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dc.creatorPolulyakh, Eugene
dc.date2000-09-16
dc.date.accessioned2026-07-07T04:37:27Z
dc.date.available2026-07-07T04:37:27Z
dc.descriptionTheorem 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.
dc.identifierhttps://arxiv.org/abs/math/0009164
dc.identifierhttp://arxiv.org/abs/math/0009164
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/59952
dc.subjectGeometric Topology
dc.subjectGeneral Topology
dc.subject14E35; 57M50; 57N35
dc.titleOn the theorem converse to Jordan's curve theorem
dc.typetext

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