完备De Morgan代数上弱余拓扑的确定

证明了对每个给定的完备De Morgan代数L,可以在WI(L)(即L上弱内部算子的全体)、WE(L)(即L上弱外部算子的全体)上定义适当的序关系,使它们成为与(WCT(L),)(即L上弱余拓扑的全体)同构的完备格;当L满足一定附加条件时,可以在WR(L)(即L上弱远域算子的全体)、WB(L)(即L上弱边界算子的全体)和WD(L)(即L上弱N-导算子的全体)上定义适当的序关系,使它们成为与(WCT(L),)同构的完备格.因此一个给定的完备De Morgan代数L上的弱余拓扑可以由L上的弱内部算子、弱外部算子、弱远域算子、弱边界算子或弱N-导算子.

Determination of weak cotopologies on a complete De Morgan algebra

Given complete De Morgan algebra L is proved,appropriate order relations can be defined on WI（L）（the set of all weak interior operators on L）,WE（L）（the set of weak exterior operators on L） such that WI（L） and WE（L） are both complete lattices which are isomorphic with（WCT（L）,lohtain in）（the set of weak cotopologies on L）;It is also proved that,for a given complete De Morgan algebra L which satisfies some additional conditions,appropriate order relations can be defined on WR（L）（the set of weak R-neighborhood operators on L）,WB（L）（the set of weak boundary operators on L）,and WD（L）（the set of weak N-derived operators on L）,respectively,to make WR（L）,WB（L） and WD（L） be complete lattices that are isomorphic to（WCT（L）,lohtain in）.Thus a weak cotopology on a given complete De Morgan algebra L can be determined by a weak interior operator,a weak exterior operator,a weak R-neighborhood operator,a weak boundary opertor,or a weak N-derived operator.