The constructive Jordan curve theorem
The constructive Jordan curve theorem
复制标题
建设性乔丹曲线定理
DOI：
--
复制
发表时间：
1975
期刊：
影响因子：
--
通讯作者：
F. Richman
中科院分区：
文献类型：
--
作者：
G. Berg;W. Julian;R. Mines;F. Richman
本文给出了若当曲线定理的构造性处理。它表明，给定一个约旦曲线，和一个点的距离曲线是积极的，那么有一个有限的程序来决定是否点是内部或外部的曲线。此外，给定两个点要么都在曲线内部，要么都在曲线外部，那么就有一个有限过程来构建连接这两个点的多边形路径，该路径以曲线为界。最后，给出了构造曲线内点的有限过程。
This paper presents a constructive treatment of the Jordan curve theorem. It is shown that, given a Jordan curve, and a point whose distance to the curve is positive, then there is a finite procedure to decide whether the point is inside or outside the curve. Also, given two points that are either both inside, or both outside, the curve, then there is a finite procedure that constructs a polygonal path joining the two points, that is bounded away from the curve. Finally, a finite procedure is given for constructing a point inside the curve.