Disasters in topology without the axiom of choice

DOI10.1007/S001530100094zbMath1027.03040OpenAlexW2017523153WikidataQ114018325 ScholiaQ114018325MaRDI QIDQ1407509

Kyriakos Keremedis

Publication date: 16 September 2003

Published in: Archive for Mathematical Logic (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s001530100094

zbMATH Keywords

compactcountably compactfirst countableseparablemetrizableaxiom of choice ACcountable axiom of choice CACcountable axiom of multiple choice CMC

Mathematics Subject Classification ID

Compactness (54D30) Baire category, Baire spaces (54E52) Consistency and independence results in general topology (54A35) Axiom of choice and related propositions (03E25)

Related Items (11)

On first and second countable spaces and the axiom of choice ⋮ Kinna-Wagner selection principles, axioms of choice and multiple choice ⋮ Compact complement topologies and k-spaces ⋮ Countable products and countable direct sums of compact metrizable spaces in the absence of the Axiom of Choice ⋮ Cuf products and cuf sums of (quasi-) metrizable spaces in ZF ⋮ On \(P\)-spaces and \(G_{\delta}\)-sets in the absence of the axiom of choice ⋮ On the relation of three theorems of functional analysis to the axiom of choice ⋮ Reverse mathematics of topology: dimension, paracompactness, and splittings ⋮ On sequentially compact subspaces of \(\mathbb R\) without the axiom of choice ⋮ Pincherle's theorem in reverse mathematics and computability theory ⋮ Countable compact Hausdorff spaces need not be metrizable in ZF

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