Countable Compact Scattered T2Spaces and Weak Forms of AC

DOI10.4064/ba54-1-7zbMath1115.03066OpenAlexW1999540294MaRDI QIDQ3414705

Kyriakos Keremedis, Evangelos Felouzis, Eleftherios Tachtsis

Publication date: 10 January 2007

Published in: Bulletin of the Polish Academy of Sciences Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4064/ba54-1-7

zbMATH Keywords

Baire spacesscattered spacesaxiom of choicecompact spacesHausdorff spacescountable spacesmetrizable spaceszero-dimensional spacesweak forms of axiom of choice

Mathematics Subject Classification ID

Compactness (54D30) Metric spaces, metrizability (54E35) Lower separation axioms ((T_0)--(T_3), etc.) (54D10) Scattered spaces (54G12) Special constructions of topological spaces (spaces of ultrafilters, etc.) (54D80) Axiom of choice and related propositions (03E25)

Related Items (6)

Countable products and countable direct sums of compact metrizable spaces in the absence of the Axiom of Choice ⋮ On Hausdorff operators in ZF$\mathsf {ZF}$ ⋮ Three‐space type Hahn‐Banach properties ⋮ On iso-dense and scattered spaces without \textbf{AC} ⋮ Infinite Hausdorff spaces may lack cellular families or discrete subsets of cardinality \(\aleph_0\) ⋮ Cellularity of infinite Hausdorff spaces in \textbf{ZF}

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