On the relative strength of forms of compactness of metric spaces and their countable productivity in \(\mathbf {\text{ZF}}\)

DOI10.1016/J.TOPOL.2012.08.003zbMath1254.54032OpenAlexW2068179599MaRDI QIDQ714742

Kyriakos Keremedis

Publication date: 11 October 2012

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

Full work available at URL: https://doi.org/10.1016/j.topol.2012.08.003

zbMATH Keywords

compactcountably compactcompleteselectivesequentially compactAxiom of choiceCantor completecountable Tychonoff productsLoebtotally bounded metric spaces

Mathematics Subject Classification ID

Metric spaces, metrizability (54E35) Compact (locally compact) metric spaces (54E45) Axiom of choice and related propositions (03E25)

Related Items (10)

On metric spaces where continuous real valued functions are uniformly continuous in \(\mathbf{ZF}\) ⋮ On Sequential Compactness and Related Notions of Compactness of Metric Spaces in $\mathbf {ZF}$ ⋮ \(k\)-spaces, sequential spaces and related topics in the absence of the axiom of choice ⋮ Some versions of second countability of metric spaces in ZF and their role to compactness ⋮ Some Notions of Separability of Metric Spaces in $\mathbf {ZF}$ and Their Relation to Compactness ⋮ On iso-dense and scattered spaces without \textbf{AC} ⋮ On pseudocompactness and light compactness of metric spaces in $\mathbf {ZF}$ ⋮ Second-countable compact Hausdorff spaces as remainders in \textbf{ZF} and two new notions of infiniteness ⋮ On densely complete metric spaces and extensions of uniformly continuous functions in $\mathbf{ZF}$ ⋮ On Loeb and sequential spaces in \textbf{ZF}

Cites Work

• On sequentially compact subspaces of \(\mathbb R\) without the axiom of choice
• Countable choice and pseudometric spaces
• Compact Metric Spaces and Weak Forms of the Axiom of Choice
• Horrors of Topology Without AC: A Nonnormal Orderable Space
• Consequences of the failure of the axiom of choice in the theory of Lindelöf metric spaces
• Weak axioms of choice for metric spaces
• A New Proof of the Tychonoff Theorem
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