Abstract
A model of a \(T_1\) topological space X is a poset P such that the set of maximal points of P with the relative Scott topology is homeomorphic to X. In this paper, we prove that (i) a \(T_1\) space is Baire if and only if it has a dcpo model whose Scott space is Baire; (ii) a \(T_1\) space is Choquet complete iff it has a dcpo model whose Scott space is Choquet complete; (iii) a \(T_1\) space has a quasicontinuous dcpo model iff it has a continuous dcpo model.
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He, Q., Xi, X. & Zhao, D. Dcpo Models of Choquet Complete and Baire Spaces. Results Math 74, 87 (2019). https://doi.org/10.1007/s00025-019-1011-1
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DOI: https://doi.org/10.1007/s00025-019-1011-1