Spatiality of countably presentable locales (proved with the Baire category theorem)
Spatiality of countably presentable locales (proved with the Baire category theorem)
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DOI：
10.1017/s0960129513000418
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发表时间：
2015-10-01
影响因子：
0.5
通讯作者：
Heckmann, Reinhold
中科院分区：
文献类型：
--
作者：
Heckmann, Reinhold
本文第一部分对著名的贝尔范畴定理进行了推广。推广就是将原公式中的密集开集替换为密集UCO集，其中UCO表示封闭与开放的并集。这一拓扑定理正是本文第二部分所需要证明的区域论结果，即开放的框架具有可数表示（可数生成子和可数关系）的区域是空间的。这个空间性定理不需要选择。
The first part of the paper presents a generalization of the well-known Baire category theorem. The generalization consists in replacing the dense open sets of the original formulation by dense UCO sets, where UCO means union of closed and open. This topological theorem is exactly what is needed to prove in the second part of the paper the locale-theoretic result that locales whose frame of opens has a countable presentation (countably many generators and countably many relations) are spatial. This spatiality theorem does not require choice.