交S-超连续偏序集
发布时间：2018-10-17 13:18
【摘要】：利用偏序集上的Scott S-集,引入了交S-超连续偏序集概念,探讨了交S-超连续偏序集的性质、刻画及与S-超连续偏序集、拟S-超连续偏序集等之间的关系。主要结果有:(1)交S-超连续的格一定是分配格;(2)有界完备偏序集(简记为bc-poset)L是交S-超连续的当且仅当对任意x∈L及子集A,当∨A存在时有x∧∨A=∨{x∧a:a∈A};(3)有界完备偏序集S-超连续的当且仅当它是交S-超连续且拟S-超连续的;(4)获得了反例说明分配的完备格可以不是交S-超连续格,连续格也可以不是交S-超连续格。
[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，
本文编号：2276779
[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，
本文编号：2276779
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