Xi-Zhao Model Preserves WD Spaces

2023/11/14 by Siheng Chen, Qingguo Li, Chen, Siheng +1
Mathematics · #Advanced Topics in Algebra #Advanced Topology and Set Theory #FOS: Mathematics #General Topology (math.GN) #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2311.07949

openalex publication_date 2023/11/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a T₁ space X, Zhao and Xi constructed a dcpo model P, where P is a bounded complete algebraic poset model of X. In this paper, we formulate the closed WD subsets of the maximal point space Max(P) and the Scott space ΣP, and then prove that X is a WD space if and only if ΣP is a WD space. It is also shown that the sobrification X^s (resp., the well-filtered reflection X^w) of X can be embedded into the sobrification P^s (resp., the well-filtered reflection P^w) of P as a saturated subspace. Finally, we introduce two new concepts ``\rm H-model spaces" and ``weak \rm H-model spaces", and provide a general framework to prove that such T₁ spaces can be preserved by Xi-Zhao dcpo models.

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