完备格中的收敛理论

On the Convergence in Complete Lattices

研究了完备格中的完备子集与Ｍｏｏｒｅ－Ｓｍｉｔｈ收敛，Ｃａｒｔａｎ的Ｆｉｌｔｅｒ收敛之间的关系．讨论了在完备格中，内部算子与完备子集的等价性，Ｍｏｏｒｅ－Ｓｍｉｔｈ收敛与Ｆｉｌｔｅｒ收敛的等价性，收敛类与完备子集的等价性．最后得到收敛与完备子集等价的结论，将Ｋｅｌｌｅｙ的结果推广到了完备格上，改进了前人已有的结果．

Kelley studied Moors-smith convergence in a topological space and showedthat the topology of a space can be described completely in terms of convergence.relationships among the complete subset Moors-smith convergence and Cartan Filterconvergence in a complete lattice are investigated. Several theorems are obtained. Theequivalence of the interior operator and the complete subset are studied. Moors-smithconvergence and Filter convergence, Moor-smithconvergence and the complete subset are discussed. As a result the complete subset finally got is practically equivalent with theconvergence. Thus Kelley's conclusion is extended to the complete lattices and theresults got by our predecessors are improved.