邻域和开集拓扑溯源与四色问题构造法逻辑证明  

Topology Tracing of Neighborhood and Open Set and Logical Proof of Four-color Problem Construction Method

作　　者：崔岩[1] 崔朝栋[2] Cui Yan;Cui Chaodong(School of Computer Science and Engineering,North China Institute of Aerospace Engineering,Langfang 065000,China;Construction Mechanization Research Branch,China Academy of Building Research,Langfang 065000,China)

机构地区：[1]北华航天工业学院计算机学院,河北廊坊065000 [2]中国建筑科学研究院建筑机械化研究分院,河北廊坊065000

出　　处：《北华航天工业学院学报》2024年第2期5-8,共4页Journal of North China Institute of Aerospace Engineering

摘　　要：在分析邻域和开集的定义、性质基础上,针对拓扑学对二者的等价描述、相互包含涵义、开集特征等问题,对邻域和开集展开拓扑溯源,提出可以刻画出二者特性的二象函数e^(x)。针对地图四色问题的拓扑性质,提出用对称点同色法着色原理的构造法逻辑证明四色问题的简捷方法。On the basis of analyzing the definitions and properties of neighborhood and open set,aiming at the equivalent description,mutual inclusion meaning and open set characteristics of the two problems in topology,the derivation of neighborhood and open set is expanded topologically,and a binary function is proposed which can describe the characteristics of both.Aiming at the topological property of the four-color problem of map,a simple method is proposed to prove the four-color problem by constructing the coloring principle of the same color method with symmetrical points.

关 键 词：二象函数 对称点 同色法 构造法 

分 类 号：O157.9[理学—数学]