On the Compactness and Countable Compactness of $2^{\mathbb{R}}$ in ZF

Volume 55 / 2007

Kyriakos Keremedis, Evangelos Felouzis, Eleftherios Tachtsis Bulletin Polish Acad. Sci. Math. 55 (2007), 293-302 MSC: 03E25, 54A35, 54B10, 54D20, 54D30. DOI: 10.4064/ba55-4-1

Abstract

In the framework of ZF (Zermelo–Fraenkel set theory without the Axiom of Choice) we provide topological and Boolean-algebraic characterizations of the statements “$2^{\mathbb{R}}$ is countably compact” and “$2^{\mathbb{R}}$ is compact”

Authors

  • Kyriakos KeremedisDepartment of Mathematics
    University of the Aegean
    Karlovassi, 83200, Samos, Greece
    e-mail
  • Evangelos FelouzisDepartment of Mathematics
    University of the Aegean
    Karlovassi, 83200, Samos, Greece
    e-mail
  • Eleftherios TachtsisDepartment of Statistics
    and Actuarial-Financial Mathematics
    University of the Aegean
    Karlovassi, 83200, Samos, Greece
    e-mail

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