摘要
在完备格中引入了元素的成分概念．基于此，引入了元素的宽度的概念．在分配格的情形证明了元素的成分集对有限并运算封闭且有某种遗传性．证明了元素的有限宽度的成分之集是定向集．称没有非平凡成分的元素为颗粒．称每个非零元素都可表示为其颗粒成分之并的完备格为颗粒表示格．证明了拓扑空间是局部连通的充要条件是其开集格为颗粒表示格．
The concept of component and width of element of complete lattices are introduced.It is proved therefrom that the set of components of any element is closed under the operation of finite unions and the set of components with finite width of any element is directed.Elements without proper component are called granules.A complete lattice is called a granule representable lattice if every non-zero element is the union of all its granular components.It is proved that a topological space is locally connected if and if the lattice consisting of all its open sets is a granule representable lattice.
出处
《数学学报（中文版）》
SCIE
CSCD
北大核心
2001年第5期829-836,共8页
Acta Mathematica Sinica：Chinese Series
基金
国家自然科学基金重点项目(19831040)
