地图空间认知的数学原理  

The mathematical principle of cognition in map space

作　　者：钟业勋[1] 朱重光[2] 魏文展[1] 

机构地区：[1]广西师范学院数学与信息科学研究所,南宁530001 [2]中国科学院遥感应用研究所,北京100101

出　　处：《测绘科学》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)

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.

关 键 词：双一一函数 制图物体 地图符号 同胚 空间认知 

分 类 号：P28[天文地球—地图制图学与地理信息工程]