拓扑格、(拟)闭包、(拟)内部及对偶方法

Topological Lattices,(Quasi-) Closures,(Quasi-) Interiors and Duality Methods

用对偶原理讨论了完全分配格L上（拟）闭包及（拟）内部运算的性质，证明了格上的开、闭拓扑、学在非F格情形等价，深化了现行的相关结果．特别，对L上的拟闭包（拟内部）运算引入了一种等价关系，证明了同一等价类中的所有运算导出同一闭（开）拓扑，并证明了任一等价类中恰有一个元是闭包（内部）运算且是该类中的最大（最小）元．

By the duality principle, we discuss the properties of （quasi-）closure operations and （quasi-）interior operations on completely distributive lattice L, prove that two （open and closed） theories of topology on lattice are equivalent to each other when lattices are not F-lattices, and deepen the current correlated results. Particularly, we introduce an equivalent relation on the whole of quasi-closure （quasi-interior） operations on L, prove that all operations in each equivalent class derive the same closed （open） topology, and prove that there exists exactly one closure （interior） operation that is the greatest （least） element in each equivalent class.