Separable connected metric spaces need not have continuum size in \(\mathbf{ZF}\)

DOI10.1016/J.TOPOL.2013.11.002zbMath1283.54020OpenAlexW1968371251MaRDI QIDQ386227

Kyriakos Keremedis, Horst Herrlich

Publication date: 9 December 2013

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

Full work available at URL: https://doi.org/10.1016/j.topol.2013.11.002

zbMATH Keywords

axiom of choiceconnected separable metric spaceMenger-Moore-Mazurkiewicz theorempunctiformtotally imperfect

Mathematics Subject Classification ID

Continua and generalizations (54F15) Metric spaces, metrizability (54E35) Compact (locally compact) metric spaces (54E45) Connected and locally connected spaces (general aspects) (54D05) Counterexamples in general topology (54G20) Axiom of choice and related propositions (03E25)

Related Items (1)

Stranger things about the cardinality of compact metric spaces without AC

Cites Work

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• Continuing horrors of topology without choice
• Compact Metric Spaces and Weak Forms of the Axiom of Choice
• Decomposable cardinals.
• A New Proof of the Tychonoff Theorem
• Connected and disconnected plane sets and the functional equation 𝑓(𝑥)+𝑓(𝑦)=𝑓(𝑥+𝑦)
• Axiom of choice
• The axiom of choice

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