摘要
ＴｈｅＥｘｉｓｔｅｎｃｅｏｆｔｈｅＣｏｍｐｌｅｔｅａｎｄＣｏｍｐｌｅｔｅｌｙＤｉｓｔｒｉｂｕｔｉｖｅＬａｔｔｉｃｅｓＢａｔＲｕｉｐｕ（白瑞蒲）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＨｅｂｅｉＵｎｉｖｅｒｓｉｔｙ，Ｂａｏｄｉｎｇ，０７１００...
The existence of some lattices and the lattice having the smallest set of generating elements are important in lattice theory. In this paper by means of the relations of the intrinsic topologies and admissible topology of a lattice,we prove there not exists the in flute complete and completely distributive lattice which has finite dimension.A complete boolean lattice B possesses the smallest set of generating elements iff B is completely distributive.
关键词
完全分配格
存在性
拓扑格
topological lattice
smallest set of generating elements
intrinsic topology
