THE SCOTT TOPOLOGY AND LAWSON TOPOLOGY ON A Z-QUASICONTINUOUS DOMAIN
THE SCOTT TOPOLOGY AND LAWSON TOPOLOGY ON A Z-QUASICONTINUOUS DOMAIN
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发表时间：
2003
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通讯作者：
Liu Ying-Ming
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作者：
Liu Ying-Ming
对于一般的子集系统Z，引入了Z-拟连续整环的概念，证明了下列结果：(1)Z-完备偏序集P是Z-拟连续的当且仅当P的所有Z-Scott开子集的完备格是超连续的；(2)Z-拟连续偏序集P上的Z-Scott拓扑σZ(P)是清醒的当且仅当σZ(P)具有Rudin性；(3)具有Z-λ拓扑的Z-拟连续偏序集P是正空间.进一步地，如果P的所有上Z-Lawson开子集都是Z-Scott开子集，且P的所有下Z-Lawson开子集在(P，w(P))中都是开的，则(P，λZ(P))是严格完全正则序空间。
For a general subset system Z, the concept of a Z-quasicontinuous domain is introduced, and the following results are proved: (1) a Z-complete poset P is Z-quasicontinuous if and only if the complete lattice of all Z-Scott open subsets of P is hypercontinuous, (2) the Z-Scott topology σZ(P) on a Z-quasicontinuous poset P is Sober if and only if σZ(P) has the Rudin property, and (3) a Z-quasicontinuous poset P endowed with the Z-Lawson topology λZ(P) is a pospace. Furthermore, if all upper Z-Lawson open subsets of P are Z-Scott open and all lower Z-Lawson open subsets of P are open in (P, w(P)), then (P, λZ(P)) is a strictly completely regular ordered space.