用L-预远域系算子、L-预外部算子或L-预边界算子确定L-预拓扑

Determining an L-pretopology by an L-pre-R-neighborhood System Operator,by an L-preexterior Operator,or by an L-preboundary Operator

给定集合X,设T(X)是X上的L-预拓扑的全体。本文证明了可以在R(X)(X上的L-预远域系算子的全体)、E(X)(X上的L-预外部算子的全体)和B(X)(X上的L-预边界算子的全体)上定义适当的序关系,使它们在一定条件下成为与(T(X),)同构的完备格。因此一个给定集合X上的L-预拓扑可以由X上的L-预远域系算子、L-预外部算子或L-预边界算子确定。

For an abitrary set X, appropriate order relations on R （X） （the set of all L-pre-R-neighborhood system operators）, E（X） （the set of all L-preexterior operators）, and B（X） （the set of all L-preboundary operators） can be defined respectively to make R （X）, E （X）, and B （X） be complete lattices that are ismorphic to （T（X）, belong to） （where T（X） is the set of all L-pretopologies on X）. Thus an L-pretopology on a given set X can be determined by an L-pre - R - neighborhood system operator, by an L-preexterior operator, or by an L-preboundary operator.