Jordan curve theorem

Noun

 * 1)  The theorem that states that a simple closed curve (Jordan curve) divides the plane into precisely two distinct areas.
 * 2) * 2009, Josef Šlapal, Jordan Curve Theorems with Respect to Certain Pretopologies on $$\mathbb{Z}^2$$, Srecko Brlek, Christophe Reutenauer, Xavier Provençal (editors), Discrete Geometry for Computer Imagery: 15th IAPR International Conference, Springer, LNCS 5810, page 252,
 * Some known Jordan curves in the basic topology are used to prove Jordan curve theorems that identify Jordan curves among simple closed ones in each of the four quotient pretopologies.
 * 1) * 2009, Josef Šlapal, Jordan Curve Theorems with Respect to Certain Pretopologies on $$\mathbb{Z}^2$$, Srecko Brlek, Christophe Reutenauer, Xavier Provençal (editors), Discrete Geometry for Computer Imagery: 15th IAPR International Conference, Springer, LNCS 5810, page 252,
 * Some known Jordan curves in the basic topology are used to prove Jordan curve theorems that identify Jordan curves among simple closed ones in each of the four quotient pretopologies.
 * 1) * 2009, Josef Šlapal, Jordan Curve Theorems with Respect to Certain Pretopologies on $$\mathbb{Z}^2$$, Srecko Brlek, Christophe Reutenauer, Xavier Provençal (editors), Discrete Geometry for Computer Imagery: 15th IAPR International Conference, Springer, LNCS 5810, page 252,
 * Some known Jordan curves in the basic topology are used to prove Jordan curve theorems that identify Jordan curves among simple closed ones in each of the four quotient pretopologies.