用弱孤立算子或弱外孤立算子确定闭包系统

Determining a closure system by a weak isolated operator or a week outer isolated operator

引入了弱孤立算子和弱外孤立算子的概念,证明了对每个给定的集合X,可以给WI(X)(X上弱孤立算子的全体)和WOI(X)(X上的弱外孤立算子的全体)上赋予适当的序关系≤,使得(WI(X),≤)和(WOI(X),≤■)是与(CS(X),)同构的完备格,这里CS(X)是X上的闭包系统的全体.因此可以用弱孤立算子或弱外孤立算子确定闭包系统.

The notions of weak isolated operator and weak outer isolated operator are introduced in this paper. It is proved that,for a given set X,appropriate order relations ≤ can be defined on WI（X）（the set of all weak isolated operators on X）and WOI（X） （the set of all weak outer isolated operaters on X）,respectively,such that both （WI（X）,≤）and （WOI（X）,≤）are complete lattices which are iso- morphic to （CS（X）,）（the set of all closure systems on the set X）. Therefore,one can determin a closure system by a weak isolated operator or by a weak outer isolated operator.