Cartesian closed categories of FƵ-domains
Cartesian closed categories of FƵ-domains
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DOI：
10.1007/s10114-013-1240-2
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发表时间：
2013-11
期刊：
影响因子：
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通讯作者：
Min Liu;Bin Zhao
中科院分区：
文献类型：
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作者：
Min Liu;Bin Zhao
子集systemZ将某些子集集合Z(P)分配给每个部分有序集合Pa。本文介绍了一种新的子集系统，称为可定向子集系统。对于可定向子集系统Ƶ，引入FƵ路下关系和FƵ域的概念。众所周知的 Scott 拓扑自然地推广到Ƶ-级别，所得拓扑称为 FƵ-Scott 拓扑，并且关于该拓扑的连续函数的特征是保留有向Ƶ-集的上界。然后，我们主要考虑将有向完全偏序集的 DCPO、双有限域的 BF 和 FS 域的 FS 的笛卡尔封闭性推广到Ƶ 级。与它们相对应，证明了对于一个合适的子集系统Ƶ，Ƶ-完全偏集的类别FƵCPO、有限分离FƵ域的FSFƵ和二有限FƵ域的BFFƵ都是笛卡尔闭的。给出了这些类别的一些示例。
A subset systemZassigns to each partially ordered setPa certain collectionZ(P) of subsets. In this paper, a new kind of subset systems called directable subset systems is introduced. For a directable subset systemƵ, the concepts ofFƵ-way-below relation andFƵ-domain are introduced. The well-known Scott topology is naturally generalized to theƵ-level and the resulting topology is calledFƵ-Scott topology, and the continuous functions with respect to this topology are characterized by preserving the suprema of directedƵ-sets. Then, we mainly consider a generalization of the cartesian closedness of the categoriesDCPOof directed complete posets,BFof bifinite domains andFSofFS-domains to theƵ-level. Corresponding to them, it is proved that, for a suitable subset systemƵ, the categoriesFƵCPOofƵ-complete posets,FSFƵof finitely separatedFƵ-domains andBFFƵof bifiniteFƵ-domains are all cartesian closed. Some examples of these categories are given.