KnowraJordan curve theoremLinked fromLinked fromThe 21 pages that link to Jordan curve theorem, each with the reason it gives.All 21Broader topic 1Related 16Narrower topic 1Compared with 3Cauchy's integral formulaRelated: It gives a precise meaning to the interior enclosed by the formula’s simple contour.Four color theoremRelated: It supports the topological reasoning behind boundaries and regions in planar maps.Connected spaceRelated: It studies how a connected curve creates a separation of its surrounding space.Cauchy's integral theoremRelated: It formalizes the inside and boundary geometry used in common versions of the theorem.Closed curveRelated: It states the key separation property of simple planar loops.Alexander horned sphereRelated: The horned sphere extends the separation theme to a setting where complement topology becomes subtler.Planar separator theoremRelated: A cycle separator divides embedded vertices because its curve separates the plane.Invariance of domainRelated: Separation ideas in the plane illuminate why injective maps preserve local openness.Pasch's axiomRelated: Both concern separation in the plane, though the theorem requires substantially deeper machinery.Schoenflies problemRelated: It is the two-dimensional separation result generalized by Schoenflies questions.Arthur Moritz SchoenfliesRelated: Schoenflies investigated the stronger question of how the curve’s regions relate to a disk.Fáry's theoremRelated: Its separation principle underlies reasoning about faces and crossings in planar drawings.Pick's theoremRelated: Its notion of an enclosed interior underlies the theorem's count I.Erdős–Nagy theoremRelated: A simple polygon has a well-defined bounded interior to convexify.Holditch's theoremRelated: It clarifies when a traced closed curve encloses a well-defined inside region.Three utilities problemRelated: Separation by closed curves underlies intuitive proofs that the required paths cannot all fit.
KnowraJordan curve theoremLinked fromLinked fromThe 21 pages that link to Jordan curve theorem, each with the reason it gives.All 21Broader topic 1Related 16Narrower topic 1Compared with 3Cauchy's integral formulaRelated: It gives a precise meaning to the interior enclosed by the formula’s simple contour.Four color theoremRelated: It supports the topological reasoning behind boundaries and regions in planar maps.Connected spaceRelated: It studies how a connected curve creates a separation of its surrounding space.Cauchy's integral theoremRelated: It formalizes the inside and boundary geometry used in common versions of the theorem.Closed curveRelated: It states the key separation property of simple planar loops.Alexander horned sphereRelated: The horned sphere extends the separation theme to a setting where complement topology becomes subtler.Planar separator theoremRelated: A cycle separator divides embedded vertices because its curve separates the plane.Invariance of domainRelated: Separation ideas in the plane illuminate why injective maps preserve local openness.Pasch's axiomRelated: Both concern separation in the plane, though the theorem requires substantially deeper machinery.Schoenflies problemRelated: It is the two-dimensional separation result generalized by Schoenflies questions.Arthur Moritz SchoenfliesRelated: Schoenflies investigated the stronger question of how the curve’s regions relate to a disk.Fáry's theoremRelated: Its separation principle underlies reasoning about faces and crossings in planar drawings.Pick's theoremRelated: Its notion of an enclosed interior underlies the theorem's count I.Erdős–Nagy theoremRelated: A simple polygon has a well-defined bounded interior to convexify.Holditch's theoremRelated: It clarifies when a traced closed curve encloses a well-defined inside region.Three utilities problemRelated: Separation by closed curves underlies intuitive proofs that the required paths cannot all fit.