topology, the Jordan curve theorem (JCT), formulated by Camille Jordan in 1887, asserts that every Jordan curve (a plane simple closed curve) divides the...

problem or Schoenflies theorem, of geometric topology is a sharpening of the Jordan curve theorem by Arthur Schoenflies. For Jordan curves in the plane it is...

are multiple theorems named after the French mathematician Camille Jordan: The Jordan curve theorem states that every simple closed curve has a well-defined...

remain specific to curves, such as space-filling curves, Jordan curve theorem and Hilbert's sixteenth problem. A topological curve can be specified by...

number of results: The Jordan curve theorem, a topological result required in complex analysis The Jordan normal form and the Jordan matrix in linear algebra...

In vector calculus, Green's theorem relates a line integral around a simple closed curve C to a double integral over the plane region D (surface in R 2...

use the Jordan curve theorem, which states that any open curve that starts and ends outside of a closed curve must intersect the closed curve an even...

one of the key theorems characterizing the topology of Euclidean spaces, along with the Jordan curve theorem, the hairy ball theorem, the invariance...

Together τn and f ∘ γrn form a simple Jordan curve. Its interior Un is contained in U by the Jordan curve theorem for ∂U and ∂Un: to see this, notice that...

residue theorem, sometimes called Cauchy's residue theorem, is a powerful tool to evaluate line integrals of analytic functions over closed curves; it can...

inequality Jordan curve Jordan curve theorem Knot Limit cycle Linking coefficient List of circle topics Loop (knot) M-curve Mannheim curve[2] Meander...

meeting at a common endpoint, and no other intersections. By the Jordan curve theorem, it separates the plane into two regions, one of which (the interior...

by the Jordan curve theorem. By contrast, for a regular star polygon {p/q}, the density is q. Turning number cannot be defined for space curves as degree...

closed curve admits a well-defined interior, which follows from the Jordan curve theorem. The inner loop of a beltway road in a country where people drive...

empty). The interior and exterior of a closed curve are a slightly different concept; see the Jordan curve theorem. If S {\displaystyle S} is a subset of a...

field at the endpoints of the curve. The theorem is a generalization of the second fundamental theorem of calculus to any curve in a plane or space (generally...

Wilhelm Jordan is not to be confused with the French mathematician Camille Jordan (Jordan curve theorem), nor with the German physicist Pascual Jordan (Jordan...

\gamma :[a,b]\to \mathbb {R} ^{2}} be a piecewise smooth Jordan plane curve. The Jordan curve theorem implies that γ {\displaystyle \gamma } divides R 2 {\displaystyle...

the Jordan curve theorem in 1905; while this was long considered the first rigorous proof of the theorem, many now also consider Camille Jordan's original...

they divide a plane into interior and exterior parts. Known as the Jordan curve theorem, it exemplifies a mathematical proposition easily stated but difficult...

convex curve. When a bounded convex set in the plane is not a line segment, its boundary forms a simple closed convex curve. By the Jordan curve theorem, a...

Surfaces in Mathifold Project The Classification of Surfaces and the Jordan Curve Theorem in Home page of Andrew Ranicki Math Surfaces Gallery, with 60 ~surfaces...

notion, Jordan in 1887 introduced the following rigorous definition, which has since been adopted as the precise description of the notion of a curve: A curve...

Hahn–Mazurkiewicz theorem (continuum theory) Heine–Borel theorem (real analysis) Heine–Cantor theorem (metric geometry) Jordan curve theorem (topology) Kuratowski's...

boundary return True if (slope < 0) != (by < ay): c = not c return c Jordan curve theorem Complex polygon Tessellation TrueType J. D. Foley, A. van Dam, S...

Hatcher's book below, theorem 1.20. Applications of the fundamental groupoid on a set of base points to the Jordan curve theorem, covering spaces, and...

Simple polygons are sometimes called Jordan polygons, because they are Jordan curves; the Jordan curve theorem can be used to prove that such a polygon...

assumption that all faces are disks is needed here, to show via the Jordan curve theorem that this operation increases the number of faces by one.) Continue...

\gamma :[a,b]\to \mathbb {R} ^{2}} be a piecewise smooth Jordan plane curve. The Jordan curve theorem implies that γ {\displaystyle \gamma } divides R 2 {\displaystyle...

3 , 3 {\displaystyle K_{3,3}} uses a case analysis involving the Jordan curve theorem. In this solution, one examines different possibilities for the locations...