Linked from

The 21 pages that link to Jordan curve theorem, each with the reason it gives.

• Cauchy'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.

• Green's theoremNarrower topic: It supplies the enclosed region whose area integral appears in Green's theorem.

• Connected spaceRelated: It studies how a connected curve creates a separation of its surrounding space.

• Winding numberCompared with: For a positively oriented simple curve, the winding number is one inside and zero outside; self-intersections allow other integers.

• Camille JordanBroader topic: Jordan proved this foundational result in topology.

• 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.

• Jordan's lemmaCompared with: It concerns what a closed curve encloses, unlike Jordan's analytic estimate on an arc.

• 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.

• Dehn's lemmaCompared with: It concerns separation in the plane, not filling a boundary curve by a disk in a 3-manifold.

• 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.