完全分配格上的極小族拓?fù)?/h1>

采用極小族理論建立了完全分配格上的另外一種拓?fù)洹獦O小族拓?fù)?，使得最大?biāo)準(zhǔn)極小族是該拓?fù)鋬H有的非平凡開(kāi)集。給出了極小族拓?fù)涞囊恍┬再|(zhì)及該拓?fù)湎潞瘮?shù)連續(xù)的必要條件，討論了該拓?fù)湎掠成涞倪B續(xù)性和廣義序同態(tài)的關(guān)系，證明了完全分配格上的標(biāo)準(zhǔn)極小族映射為廣義序同態(tài)。
關(guān) 鍵 詞 完全分配格; 極小族; 最大標(biāo)準(zhǔn)極小族; 極小族拓?fù)? 廣義序同態(tài)

Abstract In this paper, a new topological space as well as minimal families topological space is established on completely distributive lattices by using the results of the minimal families, the result that the largest standard minimal families are only nontrivial open sets on this topology is proved .The properties and the sufficient and necessary condition for functional continuity on the minimal families topological space shall be given, the relation between the continuity and the generalized order homomorphism under the new topological space is discussed, the result that the standard minimal families mapping on completely distributive lattices is the generalized order homomorphism is obtained.
Key words completely distributive lattices; minimal families; the largest standard minimal families; minimal families topology