AN ELEMENTARY GEOMETRIC NONSTANDARD PROOF OF THE JORDAN CURVE THEOREM

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dc.contributor.authorBERTOGLIO, N
dc.contributor.authorCHUAQUI, R
dc.date.accessioned2025-01-21T01:35:34Z
dc.date.available2025-01-21T01:35:34Z
dc.date.issued1994
dc.description.abstractWe give an elementary proof, using nonstandard analysis, of the Jordan curve theorem. We also give a nonstandard generalization of the theorem. The proof is purely geometrical in character, without any use of topological concepts and is based on a discrete finite form of the Jordan theorem, whose proof is purely combinatorial.
dc.description.abstractSome familiarity with nonstandard analysis is assumed. The rest of the paper is self-contained except for the proof a discrete standard form of the Jordan theorem. The proof is based on hyperfinite approximations to regions on the plane.
dc.fuente.origenWOS
dc.identifier.issn0046-5755
dc.identifier.urihttps://repositorio.uc.cl/handle/11534/97697
dc.identifier.wosidWOS:A1994NZ85700002
dc.issue.numero1
dc.language.isoen
dc.pagina.final27
dc.pagina.inicio15
dc.revistaGeometriae dedicata
dc.rightsacceso restringido
dc.subject.ods03 Good Health and Well-being
dc.subject.odspa03 Salud y bienestar
dc.titleAN ELEMENTARY GEOMETRIC NONSTANDARD PROOF OF THE JORDAN CURVE THEOREM
dc.typeartículo
dc.volumen51
sipa.indexWOS
sipa.trazabilidadWOS;2025-01-12
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