【摘要】：利用偏序集上的Scott S-集,引入了交S-超連續(xù)偏序集概念,探討了交S-超連續(xù)偏序集的性質(zhì)、刻畫及與S-超連續(xù)偏序集、擬S-超連續(xù)偏序集等之間的關(guān)系。主要結(jié)果有:(1)交S-超連續(xù)的格一定是分配格;(2)有界完備偏序集(簡記為bc-poset)L是交S-超連續(xù)的當(dāng)且僅當(dāng)對任意x∈L及子集A,當(dāng)∨A存在時有x∧∨A=∨{x∧a:a∈A};(3)有界完備偏序集S-超連續(xù)的當(dāng)且僅當(dāng)它是交S-超連續(xù)且擬S-超連續(xù)的;(4)獲得了反例說明分配的完備格可以不是交S-超連續(xù)格,連續(xù)格也可以不是交S-超連續(xù)格。
[Abstract]:By using Scott S- sets on partial ordered sets, this paper introduces the concept of intersection S- supercontinuous partial ordered sets, discusses the properties, characterizations and relations with S- supercontinuous partial ordered sets, quasi S- supercontinuous partial ordered sets and so on. The main results are as follows: (1) the lattice of intersection S- supercontinuous must be distributive lattice; (2) bounded complete partially ordered set (abbreviated to bc-poset) L is intersected S- supercontinuous if and only if for any x 鈭，

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