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中文摘要：
作为半连续格上半基和局部半基在广义理想子集系统Z上的推广,引入Z-半连续格的Z-半基及局部Z-半基概念,讨论了它们的基本性质和Z-半连续格上Z-半Lawson拓扑的性质.特别地,借助于Z-半基与局部Z-半基给出了Z-半连续格的一些刻画.
英文摘要：
As a generalization of semibasis and locally semibasis on a semicontinuous lattice, Z-semibasis and lo- cally Z-semibasis on a Z-semicontinuous lattice are introduced for a generalized ideal subsets system Z. Some properties of Z-semibasis, locally Z-semibasis and Z-semi-Lawson topology on a Z-semicontinuous lattice are presented. In particular, some characterizations of Z-semicontinuous lattices with the help of Z-semibasis are given.
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