Infinite Hausdorff spaces may lack cellular families or discrete subsets of cardinality \(\aleph_0\)

DOI10.1016/j.topol.2019.106997zbMath1443.03027OpenAlexW2996548025MaRDI QIDQ1985621

Eleftherios Tachtsis

Publication date: 7 April 2020

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

Full work available at URL: https://doi.org/10.1016/j.topol.2019.106997

zbMATH Keywords

zero-dimensional spacescattered spacecellularityspreadcompact spaceweak axioms of choiceDedekind-finite setHausdorff spaceAxiom of Choicecellular familyeffectively Hausdorff spacepermutation model of ZFArelatively discrete subspacesymmetric model of ZFweakly Dedekind-finite set

Mathematics Subject Classification ID

Compactness (54D30) Consistency and independence results (03E35) Cardinality properties (cardinal functions and inequalities, discrete subsets) (54A25) Lower separation axioms ((T_0)--(T_3), etc.) (54D10) Scattered spaces (54G12) Consistency and independence results in general topology (54A35) Axiom of choice and related propositions (03E25)

Related Items (6)

Cuf products and cuf sums of (quasi-) metrizable spaces in ZF ⋮ Models of \textsf{ZFA} in which every linearly ordered set can be well ordered ⋮ On Hausdorff operators in ZF$\mathsf {ZF}$ ⋮ Several results on compact metrizable spaces in \(\mathbf{ZF} \) ⋮ Cellularity of infinite Hausdorff spaces in \textbf{ZF} ⋮ Denumerable cellular families in \(\mathbf{ZF}\)

Cites Work

• Set theory. An introduction to independence proofs
• Countable Compact Scattered T₂Spaces and Weak Forms of AC
• Countable compact Hausdorff spaces need not be metrizable in ZF
• Subgroups of small Index in infinite Symmetric Groups
• On Countably Compact, Perfectly Normal Spaces
• Disjoint Unions of Topological Spaces and Choice
• Set Theory
• Axioms of multiple choice
• Zermelo-Fraenkel consistency results by Fraenkel-Mostowski methods
• The Tychonoff product theorem implies the axiom of choice
• The axiom of choice
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