Some independence results about compact metrizable spaces and two notions of finiteness

DOI10.1016/j.topol.2021.107947OpenAlexW4200309968MaRDI QIDQ2072140

Eleftherios Tachtsis

Publication date: 26 January 2022

Published in: Topology and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.topol.2021.107947

zbMATH Keywords

axiom of choicecompact spacemetrizable spaceweak axioms of choicesecond countable spaceseparable spaceHausdorff spacepermutation modelcuf setJech-Sochor first embedding theoremnotions of finitenessweakly Loeb spaceweakly separable space

Mathematics Subject Classification ID

Consistency and independence results (03E35) Compact (locally compact) metric spaces (54E45) Consistency and independence results in general topology (54A35) Axiom of choice and related propositions (03E25)

Related Items (3)

Countable products and countable direct sums of compact metrizable spaces in the absence of the Axiom of Choice ⋮ Stranger things about the cardinality of compact metric spaces without AC ⋮ On iso-dense and scattered spaces without \textbf{AC}

Cites Work

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• Finiteness classes and small violations of choice
• The finite and the infinite
• Quasi-metrizability of products in ZF and equivalences of CUT(fin)
• On the minimal cover property and certain notions of finite
• Continuing horrors of topology without choice
• Second-countable compact Hausdorff spaces as remainders in \textbf{ZF} and two new notions of infiniteness
• On metrizability and compactness of certain products without the axiom of choice
• Compact Metric Spaces and Weak Forms of the Axiom of Choice
• On a Certain Notion of Finite and a Finiteness Class in Set Theory without Choice
• Products of Compact Spaces in the Least Permutation Model
• On Lindelöf Metric Spaces and Weak Forms of the Axiom of Choice
• A New Proof of the Tychonoff Theorem
• Axiom of choice
• The axiom of choice

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