Matches in DBpedia 2016-04 for { <http://dbpedia.org/resource/Jordan_curve_theorem> ?p ?o }
- 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.".
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- Jordan_curve_theorem wikiPageWikiLinkText "Jordan Curve".
- Jordan_curve_theorem wikiPageWikiLinkText "Jordan arc".
- Jordan_curve_theorem wikiPageWikiLinkText "Jordan curve theorem".
- Jordan_curve_theorem wikiPageWikiLinkText "Jordan curve theorem#Generalisations".
- Jordan_curve_theorem wikiPageWikiLinkText "Jordan curve".
- Jordan_curve_theorem wikiPageWikiLinkText "Jordan curves".
- Jordan_curve_theorem wikiPageWikiLinkText "Jordan's curve theorem".
- Jordan_curve_theorem wikiPageWikiLinkText "Jordan-Brouwer".
- Jordan_curve_theorem wikiPageWikiLinkText "Jordan–Brouwer separation theorem".
- Jordan_curve_theorem wikiPageWikiLinkText "closed curve".
- Jordan_curve_theorem wikiPageWikiLinkText "generalized Jordan curve theorem".
- Jordan_curve_theorem wikiPageWikiLinkText "simple closed curve".