摘要
目的建立弱拓扑分子格的初步理论。方法运用一一对应的思想和范畴论方法研究弱余拓扑的确定和弱拓扑分子格的范畴性质。结果证明了可以用弱闭包算子确定弱余拓扑,WTML(即弱拓扑分子格与保并连续映射的范畴)和TML(即拓扑分子格与保并连续映射的范畴)都是CL(即完备格与保并映射的范畴)上的拓扑范畴。结论扩展了拓扑分子格理论。
Aim To build the theorem of weak topological molecular lattice,and discuss its properties.Methods The relation between weak closure operator and weak cotopology is studied with the help of bijection,by theorem of category,weak topological molecular lattice is discussed.Results Weak cotopology can be described by weak closure operator;and proved that both WTML（the category of weak topological molecular lattices and continuous mappings） and TML（the category of topological molecular lattices and continuous mappings） are topological categories on CL（the category of complete lattices and join-preserving mappings）.Conclusion The theorem of closure space in general topology is improved and supplemented.
出处
《西北大学学报（自然科学版）》
CAS
CSCD
北大核心
2010年第1期14-18,共5页
Journal of Northwest University（Natural Science Edition）
基金
国家自然科学基金资助项目(10271069)
陕西师范大学优秀科技预研基金资助项目(200702002)
关键词
弱拓扑分子格
弱闭包算子
连续映射
开映射
闭映射
拓扑范畴
weak topological molecular lattice
weak closure opertor
continuous mapping
open mapping
closed mapping
topological category
