复数】什么是Jordan curve[若尔当曲线]?

dodonaomikiki

谢谢~！！！

dodonaomikiki

能否以画图示之？

dodonaomikiki

en.微机pedia.org/wiki/Jordan_curve_theorem


资料！
争取弄懂！

dodonaomikiki

简单曲线通俗说来即指的是：这条曲线不和自身相交。[2]
若当定理：平面上一条闭合（首尾相接）的若尔当曲线，把平面分成2个区域，并且如果在这两个区域内分别取一点，再用一条曲线将其相连，则这条连线必定和原来的闭合若尔当曲线相交。它的证明需要用到拓扑学的知识。
若尔当曲线是以数学Jordan的名字命名，它又翻译为：若当曲线，乔丹曲线，约当曲线等

dodonaomikiki

Jordan curve theorem
From Wikipedia, the free encyclopedia

Illustration of the Jordan curve theorem. The Jordan curve (drawn in black) divides the plane into an "inside" region (light blue) and an "outside" region (pink).
In topology, a Jordan curve is a non-self-intersecting continuous loop in the plane, and another name for a Jordan curve is a plane simple closed curve.[1] 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 every 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

dodonaomikiki