On sequentially compact subspaces of \(\mathbb R\) without the axiom of choice

DOI10.1305/NDJFL/1091030855zbMath1071.03035OpenAlexW2003288973WikidataQ114007568 ScholiaQ114007568MaRDI QIDQ558740

Eleftherios Tachtsis, Kyriakos Keremedis

Publication date: 13 July 2005

Published in: Notre Dame Journal of Formal Logic (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1305/ndjfl/1091030855

zbMATH Keywords

compactnesssequential compactnessTikhonov productweak forms of the axiom of choice

Mathematics Subject Classification ID

Compactness (54D30) Sequential spaces (54D55) Axiom of choice and related propositions (03E25)

Related Items (3)

Total boundedness and the axiom of choice ⋮ On Sequential Compactness and Related Notions of Compactness of Metric Spaces in $\mathbf {ZF}$ ⋮ On the relative strength of forms of compactness of metric spaces and their countable productivity in \(\mathbf {\text{ZF}}\)

Cites Work

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• The failure of the axiom of choice implies unrest in the theory of Lindelöf metric spaces
• Sequential topological conditions in ℝ in the absence of the axiom of choice
• A New Proof of the Tychonoff Theorem
• The Tychonoff product theorem implies the axiom of choice
• The axiom of choice

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