The Relation Between Elevation of Equivalence Relation, Elevation of Distance, Hypertopology, Quotient Topology and Topological Entropy. 等价关系和距离的提升与超拓扑,商拓扑,拓扑熵间的关系。
The Elevation of Quotient Topology and Weak Topology 粘合拓扑与弱拓朴的提升
Research on the Quotient Topology 模糊商拓扑的再研究
By introducing the concept of regular equivalence relation. It is proved that quotient topology fuzzes defined by equivalence relation and continuous mapping are homeo-morphic. 通过引进正则等价关系的概念,证明了用等价关系和连续映射两种方法定义的商拓扑fuzz是同胚的。
Used the theorem of exponential correspondence, a theorem on quotient map was generalized to the cases of coinduced topology, and some applications of it in algebraic topology were also discussed. 利用指数对应定理,将关于商映射的一个定理推广到上诱导拓扑的情形,并给出其在代数拓扑学中的若干应用。
Compact quotient mapping and compact quotient topology 紧商映射与紧商拓扑
First, on the basis of the analyses for rough sets and quotient space, this dissertation constructs a topology information system. 首先以粗糙集和商空间理论为指导,构建拓扑信息系统。
Different from other granular computing theories, Quotient Space Theory introduces structure to describe topology information of universe. 商空间理论区别于其他粒计算理论,引入了结构作为研究对象的拓扑信息。