A quasi-metrization theorem for hybrid topologies on the real line in \textbf{ZF}

MaRDI QIDQ6589530

Thomas Richmond, Eliza Wajch

Publication date: 19 August 2024

Published in: Houston Journal of Mathematics (Search for Journal in Brave)

zbMATH Keywords

Sorgenfrey linereal linequasimetricquasi-metrizabilityHattori spacehybrid topology

Mathematics Subject Classification ID

Metric spaces, metrizability (54E35) Uniform structures and generalizations (54E15) Consistency and independence results in general topology (54A35)

Cites Work

• On quasi-metric spaces.
• A Dedekind finite Borel set
• On the relative strength of forms of compactness of metric spaces and their countable productivity in \(\mathbf {\text{ZF}}\)
• On Loeb and sequential spaces in \textbf{ZF}
• Continuing horrors of topology without choice
• \(k\)-spaces, sequential spaces and related topics in the absence of the axiom of choice
• Results on spaces between the Sorgenfrey and usual topologies on \(\mathbb{R}\)
• A poset of topologies on the set of real numbers.
• Criteria for Metrisability
• On Stone’s theorem and the Axiom of Choice
• Metric spaces and the axiom of choice
• General Topology
• On Hattori spaces
• Paracompactness and product spaces
• Axiom of choice
• On reversible and bijectively related topological spaces
• Hybrid topologies on the real line
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