Boole代数中极大滤子的刻画与Cantor三分集

Characterizations of Maximal Filters in Boolean Algebras and the Cantor Ternary Set

清楚地刻画出有限和由无限可数个基本元生成的Boole代数中极大滤子的具体结构,在全体极大滤子之集上通过自然的方式引入一种紧致的Hausdorff拓扑,证明了当Boole代数可由无限可数个基本元生成时所得的拓扑空间与Cantor三分集同胚.

In this paper,the concrete structure of every maximal filter in Boolean algebras which are finite or generated by infinitely countable basic elements is clearly described.In a natural way,a compact Hausdorff topology is introduced into the set of all maximal filters,and it is proved that the obtained topological space is homeomorphic to the Cantor ternary set if the Boolean algebra is generated by infinitely countable basic elements.