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arXiv · 2608.03124

The set of real numbers with the cocountable topology has a bounded complete dcpo model

Dongsheng Zhao·Chong Shen·Xiaoyong Xi
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Abstract

We construct a bounded complete dcpo P whose maximal point space is homeomorphic to the set R of all reals equipped with the cocountable topology, thereby answering an open problem. Using this dcpo, we obtain a new complete lattice whose Scott space is non-sober.

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Dongsheng Zhao, Chong Shen, Xiaoyong Xi. 2026-08-04. The set of real numbers with the cocountable topology has a bounded complete dcpo model. https://arxiv.org/abs/2608.03124

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