一般BOOLE格的古典拟拓扑开基

The Classical Quasi-Topological Open Base of a General Boolean Lattice

本文主要证明了下面的结果: 一.设II是一般Boole格L的一族容,则H是L的一个古典拟拓扑开基的充要条件为:对H的每二成分U,V及U∩的非零元x,有W∈H,使在L的完备化云中,有二.设H是古典拓扑一般Boole格<L,τ>的开基,那么对H的每二成分U,V及每元x∈U∩V(x≠0),有W∈H。

In this paper we mainly prove the following results: Theorem 1. Let H be a fancily of capacities of a general Boolean lattice L,then H is a classical quasi-topological open base iff for any U,V∈H and x∈U(?)V(x≠0),there exists a W∈H such that x∩W≠0 W≤U∩V in the completion L of L. Theorem 2. Let H be a open base of a classical topological general Boolean lattice(L,τ),then for any U,V∈H and x∈U∩V(x≠0), there exists a W∈H such that x∩W≠o, W(?)U∩V