Stranger things about the cardinality of compact metric spaces without AC

DOI10.1007/s10474-022-01272-9OpenAlexW4308965435MaRDI QIDQ2678398

Eleftherios Tachtsis, Kyriakos Keremedis

Publication date: 23 January 2023

Published in: Acta Mathematica Hungarica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10474-022-01272-9

zbMATH Keywords

compact metric spacetransfer theoremweak choice principlecardinality of compact metric spacepermutation model of ZFA+\(\overline{\text{AC}}\)

Mathematics Subject Classification ID

Metric spaces, metrizability (54E35) Consistency and independence results (03E35) Compact (locally compact) metric spaces (54E45) Cardinality properties (cardinal functions and inequalities, discrete subsets) (54A25) Connected and locally connected spaces (general aspects) (54D05) Scattered spaces (54G12) Separability of topological spaces (54D65) Axiom of choice and related propositions (03E25)

Related Items (2)

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

Cites Work

• Separable connected metric spaces need not have continuum size in \(\mathbf{ZF}\)
• Second-countable compact Hausdorff spaces as remainders in \textbf{ZF} and two new notions of infiniteness
• Several results on compact metrizable spaces in \(\mathbf{ZF} \)
• Some independence results about compact metrizable spaces and two notions of finiteness
• On metrizability and compactness of certain products without the axiom of choice
• Compact Metric Spaces and Weak Forms of the Axiom of Choice
• On Sequential Compactness and Related Notions of Compactness of Metric Spaces in $\mathbf {ZF}$
• Zermelo-Fraenkel consistency results by Fraenkel-Mostowski methods
• The axiom of choice
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