The proof of cartographic layer system belonging to boolean algebra and its application

Boolean algebra is the system where electronic computer can do logical operation. A map is the set of finite layers effectually. Layer is not only the basic storage unit of data in electronic map system, but also useful method and an efficient way in managing and organizing map data. Cartographic symbol system and cartographic image system belonging to Boolean algebra have been proved. Because layer suffices the necessary and sufficient conditions for Boolean algebra, cartographic layer system is Boolean algebra, which the computer theoretic base and mathematical tool of layer expressing in computer. Object-oriented layer stores and manages various useful data of space, attribute, symbol, annotation, legend. In electronic map and GIS layer is applied to organize data.