Displaying similar documents to “Choice principles in elementary topology and analysis”

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M. Jelić (1990)

Matematički Vesnik

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Countable Compact Scattered T₂ Spaces and Weak Forms of AC

Kyriakos Keremedis, Evangelos Felouzis, Eleftherios Tachtsis (2006)

Bulletin of the Polish Academy of Sciences. Mathematics

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We show that: (1) It is provable in ZF (i.e., Zermelo-Fraenkel set theory minus the Axiom of Choice AC) that every compact scattered T₂ topological space is zero-dimensional. (2) If every countable union of countable sets of reals is countable, then a countable compact T₂ space is scattered iff it is metrizable. (3) If the real line ℝ can be expressed as a well-ordered union of well-orderable sets, then every countable compact zero-dimensional...