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- Jordan_curve_theorem abstract "In topology, a Jordan curve is a non-self-intersecting continuous loop in the plane, and another name for a Jordan curve is a simple closed curve. The Jordan curve theorem asserts that every Jordan curve divides the plane into an "interior" region bounded by the curve and an "exterior" region containing all of the nearby and far away exterior points, so that any continuous path connecting a point of one region to a point of the other intersects with that loop somewhere. While the statement of this theorem seems to be intuitively obvious, it takes quite a bit of ingenuity to prove it by elementary means. More transparent proofs rely on the mathematical machinery of algebraic topology, and these lead to generalizations to higher-dimensional spaces. The Jordan curve theorem is named after the mathematician Camille Jordan, who found its first proof. For decades, mathematicians generally thought that this proof was flawed and that the first rigorous proof was carried out by Oswald Veblen. However, this notion has been challenged by Thomas C. Hales and others.".
- Jordan_curve_theorem thumbnail Jordan_curve_theorem.png?width=300.
- Jordan_curve_theorem wikiPageExternalLink insidepoly.
- Jordan_curve_theorem wikiPageExternalLink 4.pdf.
- Jordan_curve_theorem wikiPageExternalLink jordan.html.
- Jordan_curve_theorem wikiPageExternalLink 1102971282.
- Jordan_curve_theorem wikiPageExternalLink section5.pdf.
- Jordan_curve_theorem wikiPageExternalLink jordan.
- Jordan_curve_theorem wikiPageExternalLink jordan.pdf.
- Jordan_curve_theorem wikiPageExternalLink 17513472.2011.634320.
- Jordan_curve_theorem wikiPageExternalLink Jordan-revised.pdf.
- Jordan_curve_theorem wikiPageID "267444".
- Jordan_curve_theorem wikiPageRevisionID "597979909".
- Jordan_curve_theorem author "M.I. Voitsekhovskii".
- Jordan_curve_theorem doi "10.1007".
- Jordan_curve_theorem first "Fred".
- Jordan_curve_theorem first "Gordon O.".
- Jordan_curve_theorem first "Keita".
- Jordan_curve_theorem first "Nobuyuki".
- Jordan_curve_theorem first "R.".
- Jordan_curve_theorem first "W.".
- Jordan_curve_theorem hasPhotoCollection Jordan_curve_theorem.
- Jordan_curve_theorem id "j/j054370".
- Jordan_curve_theorem issn "35".
- Jordan_curve_theorem issn "933".
- Jordan_curve_theorem issue "5".
- Jordan_curve_theorem journal Rocky_Mountain_Journal_of_Mathematics.
- Jordan_curve_theorem journal "Archive for Mathematical Logic".
- Jordan_curve_theorem last "Berg".
- Jordan_curve_theorem last "Julian".
- Jordan_curve_theorem last "Mines".
- Jordan_curve_theorem last "Richman".
- Jordan_curve_theorem last "Sakamoto".
- Jordan_curve_theorem last "Yokoyama".
- Jordan_curve_theorem mr "2321588".
- Jordan_curve_theorem mr "410701".
- Jordan_curve_theorem pages "225".
- Jordan_curve_theorem pages "465".
- Jordan_curve_theorem title "Jordan theorem".
- Jordan_curve_theorem title "The Jordan curve theorem and the Schönflies theorem in weak second-order arithmetic".
- Jordan_curve_theorem title "The constructive Jordan curve theorem".
- Jordan_curve_theorem volume "46".
- Jordan_curve_theorem volume "5".
- Jordan_curve_theorem year "1975".
- Jordan_curve_theorem year "2007".
- Jordan_curve_theorem subject Category:Theorems_in_topology.
- Jordan_curve_theorem type Abstraction100002137.
- Jordan_curve_theorem type Communication100033020.
- Jordan_curve_theorem type Message106598915.
- Jordan_curve_theorem type Proposition106750804.
- Jordan_curve_theorem type Statement106722453.
- Jordan_curve_theorem type Theorem106752293.
- Jordan_curve_theorem type TheoremsInTopology.
- Jordan_curve_theorem comment "In topology, a Jordan curve is a non-self-intersecting continuous loop in the plane, and another name for a Jordan curve is a simple closed curve. The Jordan curve theorem asserts that every Jordan curve divides the plane into an "interior" region bounded by the curve and an "exterior" region containing all of the nearby and far away exterior points, so that any continuous path connecting a point of one region to a point of the other intersects with that loop somewhere.".
- Jordan_curve_theorem label "Jordan curve theorem".
- Jordan_curve_theorem label "Jordanscher Kurvensatz".
- Jordan_curve_theorem label "Krzywa Jordana".
- Jordan_curve_theorem label "Stelling van Jordan".
- Jordan_curve_theorem label "Teorema da curva de Jordan".
- Jordan_curve_theorem label "Teorema de la curva de Jordan".
- Jordan_curve_theorem label "Teorema della curva di Jordan".
- Jordan_curve_theorem label "Théorème de Jordan".
- Jordan_curve_theorem label "Теорема Жордана".
- Jordan_curve_theorem label "مبرهنة منحنى جوردان".
- Jordan_curve_theorem label "ジョルダン曲線定理".
- Jordan_curve_theorem label "若尔当曲线定理".
- Jordan_curve_theorem sameAs Jordanscher_Kurvensatz.
- Jordan_curve_theorem sameAs Teorema_de_la_curva_de_Jordan.
- Jordan_curve_theorem sameAs Théorème_de_Jordan.
- Jordan_curve_theorem sameAs Teorema_della_curva_di_Jordan.
- Jordan_curve_theorem sameAs ジョルダン曲線定理.
- Jordan_curve_theorem sameAs 조르당_곡선정리.
- Jordan_curve_theorem sameAs Stelling_van_Jordan.
- Jordan_curve_theorem sameAs Krzywa_Jordana.
- Jordan_curve_theorem sameAs Teorema_da_curva_de_Jordan.
- Jordan_curve_theorem sameAs m.01njzw.
- Jordan_curve_theorem sameAs Q260928.
- Jordan_curve_theorem sameAs Q260928.
- Jordan_curve_theorem sameAs Jordan_curve_theorem.
- Jordan_curve_theorem wasDerivedFrom Jordan_curve_theorem?oldid=597979909.
- Jordan_curve_theorem depiction Jordan_curve_theorem.png.
- Jordan_curve_theorem isPrimaryTopicOf Jordan_curve_theorem.