闭格与拓扑交结构  

On Closed Lattice and Topological Intersection Structure

作　　者：杨田[1] 李庆国[1] 王璐[1] 

机构地区：[1]湖南大学数学与计量经济学院,湖南长沙410082

出　　处：《湖南大学学报（自然科学版）》2007年第12期76-79,共4页Journal of Hunan University:Natural Sciences

基　　金：国家自然科学基金资助项目(10471035);高校博士点基金资助项目(2004194)

摘　　要：定义了一种新形式的格——闭格以及一种新的交结构——拓扑交结构,并证明闭格与有上界的拓扑交结构是一一对应的,闭半格与拓扑交结构也是一一对应的.从范畴的观点来看,闭格构成的范畴TL与有上界的拓扑交结构所构成的范畴TTS是范畴等价的;闭半格所构成的范畴TSL与拓扑交结构所构成的范畴TS也是范畴等价的.We introduced a new lattice closed lattice, a new intersection structure topological inter- section structure, and studied the relation between them. We have proved that there is a bijective correspon-dence between closed lattice and topped topological intersection structure as well as a closed semilattice and topological intersection structure. In the view of category theory, the category TL（closed lattice as object and continuous mapping as arrows） is equivalent to the category TTS（topped topological intersection structure as object and topological homomorphism as arrows）, and the category TSL（closed semilattice as object and continuous mapping as arrows） is equivalent to the category TS（ topological intersection structure as object and topological homomorphism as arrows）.

关 键 词：拓扑 拓扑闭包算子 闭格 拓扑交结构 并不可约元 

分 类 号：O153.1[理学—数学]