Second-countable compact Hausdorff spaces as remainders in \textbf{ZF} and two new notions of infiniteness

DOI10.1016/j.topol.2021.107732zbMath1485.03207arXiv2009.09526OpenAlexW3160800924MaRDI QIDQ2033206

Eleftherios Tachtsis, Eliza Wajch, Kyriakos Keremedis

Publication date: 14 June 2021

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

Full work available at URL: https://arxiv.org/abs/2009.09526

zbMATH Keywords

compactificationCantor setremaindermetrizabilityweak forms of the axiom of choiceUrysohn's metrization theorem

Mathematics Subject Classification ID

Metric spaces, metrizability (54E35) Consistency and independence results (03E35) Extensions of spaces (compactifications, supercompactifications, completions, etc.) (54D35) Remainders in general topology (54D40) Consistency and independence results in general topology (54A35) Local compactness, (sigma)-compactness (54D45) Axiom of choice and related propositions (03E25)

Related Items (5)

\(k\)-spaces, sequential spaces and related topics in the absence of the axiom of choice ⋮ Countable products and countable direct sums of compact metrizable spaces in the absence of the Axiom of Choice ⋮ Stranger things about the cardinality of compact metric spaces without AC ⋮ On iso-dense and scattered spaces without \textbf{AC} ⋮ Some independence results about compact metrizable spaces and two notions of finiteness

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Compactness and compactifications in generalized topology
• On the relative strength of forms of compactness of metric spaces and their countable productivity in \(\mathbf {\text{ZF}}\)
• On Loeb and sequential spaces in \textbf{ZF}
• Quasi-metrizability of products in ZF and equivalences of CUT(fin)
• Hausdorff compactifications in ZF
• Continuing horrors of topology without choice
• On metrizability and compactness of certain products without the axiom of choice
• Cellularity of infinite Hausdorff spaces in \textbf{ZF}
• A note on compactifications
• Non-discrete metrics in and some notions of finiteness
• Compact and Loeb Hausdorff spaces in \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mathsf {ZF}$\end{document} and the axiom of choice for families of finite sets
• Countable sums and products of metrizable spaces in ZF
• On Sequential Compactness and Related Notions of Compactness of Metric Spaces in $\mathbf {ZF}$
• Countable compact Hausdorff spaces need not be metrizable in ZF
• Products of Compact Spaces in the Least Permutation Model
• Spaces for which all Compact Metric Spaces are Remainders
• Adding dependent choice
• Consequences of the failure of the axiom of choice in the theory of Lindelöf metric spaces
• Products of some special compact spaces and restricted forms of AC
• A New Proof of the Tychonoff Theorem
• Zermelo-Fraenkel consistency results by Fraenkel-Mostowski methods
• Axiom of choice
• The axiom of choice

This page was built for publication: Second-countable compact Hausdorff spaces as remainders in \textbf{ZF} and two new notions of infiniteness