本文選題：Scott　切入點(diǎn)：C-集　出處：《高校應(yīng)用數(shù)學(xué)學(xué)報(bào)A輯》2017年01期 　論文類型：期刊論文

【摘要】：利用偏序集上的半拓?fù)浣Y(jié)構(gòu),引入了交C-連續(xù)偏序集概念,探討了交C-連續(xù)偏序集的性質(zhì)、刻畫(huà)及與C-連續(xù)偏序集、擬C-連續(xù)偏序集等之間的關(guān)系.主要結(jié)果有:(1)交C-連續(xù)的格一定是分配格;(2)有界完備偏序集(簡(jiǎn)記為bc-poset)L是交C-連續(xù)的當(dāng)且僅當(dāng)對(duì)任意x∈L及非空Scott閉集S,當(dāng)∨S存在時(shí)有x∧∨S=∨{x∧s:s∈S};(3)完備格是完備Heyting代數(shù)當(dāng)且僅當(dāng)它是交連續(xù)且交C-連續(xù)的;(4)有界完備偏序集是C-連續(xù)的當(dāng)且僅當(dāng)它是交C-連續(xù)且擬C-連續(xù)的;(5)獲得了反例說(shuō)明分配的完備格可以不是交C-連續(xù)格,交C-連續(xù)格也可以不是交連續(xù)格.
[Abstract]:By using the semi-topological structure of partial ordered sets, the concept of intersecting C-continuous partial ordered sets is introduced, and the properties, characterizations and properties of intersecting C-continuous partial ordered sets are discussed. Relations between quasi C- continuous partially ordered sets and so on. The main results are: 1) the lattice of intersection C- continuous must be distributive lattice / 2) bounded complete partial ordered set (abbreviated as bc-poset)L is intersected C- continuous if and only if for any x 鈭，

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