两个清醒的 dcpo 的产品不必是清醒的

arXiv - MATH - General Topology Pub Date : 2024-08-16 DOI:arxiv-2408.08587

Hualin Miao, Xiaoyong Xi, Xiaodong Jia, Qingguo Li, Dongsheng Zhao

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摘要

我们构造了两个斯科特空间清醒的 dcpo，但它们的阶乘的斯科特空间并不清醒。这回答了一个关于斯科特空间清醒度的未决问题。同时，我们证明了如果 $M$ 和 $N$ 是特殊类型的清醒完全网格，那么它们的阶乘 $M\times N$ 的斯科特空间是清醒的。

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Products of two sober dcpo's need not be sober

We constructed two dcpo's whose Scott spaces are sober, but the Scott space of their order product is not sober. This answers an open problem on the sobriety of Scott spaces. Meantime, we show that if $M$ and $N$ are special type of sober complete lattices, then the Scott space of their order product $M\times N$ is sober.

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arXiv - MATH - General Topology

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