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中文摘要：
文章引入局部相容半连续格的概念,研究其若干性质,并借助于局部相容半素极小集来阐述映射的局部相容半连续性、保lc关系和保局部相容半素极小集之间的联系.特别地,在局部相容完备格之间的Galois联络下,研究了保lc关系与（强）局部相容半连续映射之间的关系。
英文摘要：
In this paper, the concept of locally consistent semicontinuous lattices is introduced. And some properties of locally consistent semicontinuous lattices are presented. With the help of locally consistent semiprime minimal subsets, we elaborate the relationship of maps between locally consistent semicontinuous, preserving 〈=1c and preserving locally consistent semiprime minimal subsets. Especially we study the relation between preserving 〈=1c and （strongly） locally consistent semicontinuous mapping in the Galois connection of locally consistent complete lattices.
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