摘要
根据非退化区间为等势集合的原理,论证了从制图区域到二维地图平面间的映射与复合映射是双一一函数;主体意图对制图物体性质的确定,使地图符号既满足视觉感受的要求又满足制图物体Ax与地图符号pgf(Ax)之间的双一一函数关系。根据集合的连续定理,证明了地图符号pgf(Ax)是制图物体Ax的同胚象,从而为地图的空间认知提供了数学基础和理论支持。
According to the element of non-degenerate interval being equipollence set,the authors proofed that the mapping and compound mapping from the cartographic region to two-dimensional map plane are bi-jection.It makes map symbol satisfiying visual perception and bi-jection function relation between mapping object A__ and map symbol pgf(A__ ) while the character of mapping object is defined by main body intention.The authors have proofed that the map symbol pgf(A__ ) is the homeomorphism of mapping object A__ according to the theorem of set continuity which gives the mathematical basis for the space cognition of maps.
出处
《测绘科学》
CAS
CSCD
北大核心
2005年第5期11-12,共2页
Science of Surveying and Mapping
基金
广西自然科学基金资助项目(0135002)
广西科学基金项目(桂科基0448036)
