Compact Metric Spaces and Weak Forms of the Axiom of Choice

DOI<link itemprop=identifier href="https://doi.org/10.1002/1521-3870(200101)47:1<117::AID-MALQ117>3.0.CO;2-N" /><117::AID-MALQ117>3.0.CO;2-N 10.1002/1521-3870(200101)47:1<117::AID-MALQ117>3.0.CO;2-NzbMath0968.03057OpenAlexW2014507301MaRDI QIDQ2707076

Eleftherios Tachtsis, Kyriakos Keremedis

Publication date: 14 September 2001

Full work available at URL: https://doi.org/10.1002/1521-3870(200101)47:1<117::aid-malq117>3.0.co;2-n

zbMATH Keywords

separable spacecompact metric spacespermutation modelLoeb propertyweakly Loeb

Mathematics Subject Classification ID

Metric spaces, metrizability (54E35) Compact (locally compact) metric spaces (54E45) Consistency and independence results in general topology (54A35) Separability of topological spaces (54D65) Axiom of choice and related propositions (03E25)

Related Items (17)

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 ⋮ Separable connected metric spaces need not have continuum size in \(\mathbf{ZF}\) ⋮ 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 ⋮ Cuf products and cuf sums of (quasi-) metrizable spaces in ZF ⋮ On iso-dense and scattered spaces without \textbf{AC} ⋮ On metric spaces where continuous real valued functions are uniformly continuous and related notions ⋮ The independence of Stone’s Theorem from the Boolean Prime Ideal Theorem ⋮ On metrizability and compactness of certain products without the axiom of choice ⋮ On the relative strength of forms of compactness of metric spaces and their countable productivity in \(\mathbf {\text{ZF}}\) ⋮ On densely complete metric spaces and extensions of uniformly continuous functions in $\mathbf{ZF}$ ⋮ Unnamed Item ⋮ Several results on compact metrizable spaces in \(\mathbf{ZF} \) ⋮ Some independence results about compact metrizable spaces and two notions of finiteness ⋮ On Loeb and sequential spaces in \textbf{ZF}

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