Quasi-metrizability of products in ZF and equivalences of CUT(fin)

DOI10.1016/j.topol.2018.03.031zbMath1425.03020OpenAlexW2795320609WikidataQ130064672 ScholiaQ130064672MaRDI QIDQ1646538

Eliza Wajch

Publication date: 25 June 2018

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

Full work available at URL: https://doi.org/10.1016/j.topol.2018.03.031

zbMATH Keywords

compactnessproductsCantor cubesZFCC(fin)co-finite topologyquasi-metrizability

Mathematics Subject Classification ID

Metric spaces, metrizability (54E35) Consistency and independence results (03E35) Product spaces in general topology (54B10) Axiom of choice and related propositions (03E25)

Related Items (8)

Compact complement topologies and k-spaces ⋮ Countable products and countable direct sums of compact metrizable spaces in the absence of the Axiom of Choice ⋮ Cuf products and cuf sums of (quasi-) metrizable spaces in ZF ⋮ On metrizability and compactness of certain products without the axiom of choice ⋮ Hausdorff compactifications in ZF ⋮ Second-countable compact Hausdorff spaces as remainders in \textbf{ZF} and two new notions of infiniteness ⋮ Some independence results about compact metrizable spaces and two notions of finiteness ⋮ Denumerable cellular families in \(\mathbf{ZF}\)

Cites Work

• Topological equivalences of CUT and CUT(\(\mathrm{Fin}\))
• Compactness and compactifications in generalized topology
• Bitopological Spaces
• Horrors of Topology Without AC: A Nonnormal Orderable Space
• The Tychonoff product theorem implies the axiom of choice
• Axiom of choice
• The axiom of choice
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