用弱内导算子确定闭包系统

Determination a closure system by a weak interior derived operator

引入了弱内导算子概念,证明了对于每个给定的集合X,可以给WE(X)(即X上的弱内导算子的全体)上赋予适当的序关系≤使得(WE(X),≤)与(CS(X),■)完备格同构.这里CS(X)是X上的闭包系统的全体.从而它们之间也是范畴同构的,因此可以用弱内导算子完全确定闭包系统.最后讨论了弱内导算子的范畴性质.

The notion of weak interior derived operator is introduced in this paper.It is proved that,for a given set X,an order relation ≤ can be defined on WE（X）（the set of all weak interior derived operators on X） such that（WE（X）,≤） is a complete lattice which is isomorphic to（CS（X）,■）（the set of all closure systems on X）.An isomorphism also can be established between corresponding categories. Therefore,any closure system can be determined by a weak interior derived operator.Finally the properties of category of weak interior derived spaces are studied.