2023/12/06 by Vlad Smolin, Smolin, Vlad
Mathematics · #Advanced Topology and Set Theory #FOS: Mathematics #General Topology (math.GN) #Homotopy and Cohomology in Algebraic Topology #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.2312.03529
openalex publication_date 2023/12/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove that: 1. If a Hausdorff M-space is a continuous closed image of a submetrizable space, then it is metrizable. 2. A dense-in-itself open-closed image of a submetrizable space is submetrizable if and only if it is functionally Hausdorff and has a countable pseudocharacter. 3. Let Y be a dense-in-itself space with the following property: ∀ y∈ Y ∃ Q(y) ⊆ Y [y is a non-isolated q-point in Q(y)]. If Y is an open-closed image of a submetrizable space, then Y is submetrizable. 4. There exist a submetrizable space X, a regular hereditarily paracompact non submetrizable first-countable space Y, and an open-closed map f\colon X → Y.