On Meet-Continuous Dcpos
On Meet-Continuous Dcpos
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DOI：
10.1007/978-94-017-1291-0_5
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发表时间：
2003
期刊：
影响因子：
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通讯作者：
H. Kou;Ying-ming Liu;M. Luo
中科院分区：
文献类型：
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作者：
H. Kou;Ying-ming Liu;M. Luo
众所周知，完全格L是满足连续格当且仅当对于allx∈P。事实上，这个属性可以用 Scott 拓扑简单地描述为 clσ(↓x∩ ↓D) = ↓xwheneverx≤ ∨D。由于不涉及满足算子，因此满足连续性的拓扑性质可以自然地扩展到一般的dcpos。这种 dcpos 在本文中也称为连续相遇。事实证明，满足连续性、Hausdorff分离、拟连续性、连续性和Scott开滤波器基之间存在着密切的关系。特别是，我们证明Hausdorff dcpos（通过Lawson拓扑）不需要是拟连续的，类别CONT不是QCONT的反射完整子类别，准连续域的类别，并且当或者它是具有a拓扑的半格时，dcpoPi是满足连续的，其中表示由P的所有斯科特开滤波器生成的拓扑。而且，在适当的条件下，带有拓扑的dcpos范畴形成笛卡尔闭范畴。
It is well-known that a complete lattice L is a meet-continuous lattice if and only iffor allx∈P. This property in fact can be characterized by the Scott topology simply as clσ(↓x∩ ↓D) = ↓xwheneverx≤ ∨D. Since the meet operator is not involved, the topological property of meet-continuity can be naturally extended to general dcpos. Such dcpos are also called meet-continuous in this note. It turns out that there exist close relations among meet-continuity, Hausdorff separation, quasicontinuity, continuity and Scott-open filter bases. In particular, we prove that Hausdorff dcpos (via the Lawson topology) need not be quasicontinuous, the categoryCONTis not a reflective full subcategory ofQCONT, the category of quasicontinuous domains, and a dcpoPis meet-continuous whenor it is a semilattice with a-topology, wheredenote the topology generated by all the Scott-open filters ofP. Moreover, under appropriate conditions, the category of dcpos with-topology form a cartesian closed category.