On ultracompact spaces in ZF

DOI10.1016/j.topol.2019.06.039OpenAlexW2952544272MaRDI QIDQ2312459

Eleftherios Tachtsis

Publication date: 17 July 2019

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

Full work available at URL: https://doi.org/10.1016/j.topol.2019.06.039

zbMATH Keywords

hyperspacefilterultrafilteraxiom of choiceweak axioms of choicecountably compact spacefree ultrafilter\(\aleph_0\)-bounded space\(\mathcal{D}\)-compact space\(\mathcal{D}\)-limit point of sequence\(\mathcal{D}\)-pseudocompact spacesequentially limit point compact spaceultracompact spaceVietoris (finite) topology

Mathematics Subject Classification ID

Consistency and independence results (03E35) Consistency and independence results in general topology (54A35) Axiom of choice and related propositions (03E25)

Cites Work

• Some applications of ultrafilters in topology
• On a topological choice principle by Murray Bell
• On the existence of permutations of infinite sets without fixed points in set theory without choice
• The existence of free ultrafilters on ω does not imply the extension of filters on ω to ultrafilters
• On the Existence of Free Ultrafilters on ω and on Russell-sets in ZF
• On the Set-Theoretic Strength of Countable Compactness of the Tychonoff Product 2^R
• Remarks on the Stone Spaces of the Integers and the Reals without AC
• Tychonoff Products of Two-Element Sets and Some Weakenings of the Boolean Prime Ideal Theorem
• Los' Theorem and the Boolean Prime Ideal Theorem Imply the Axiom of Choice
• Some Results on the Countable Compactness and Pseudocompactness of Hyperspaces
• A new kind of compactness for topological spaces
• The Tychonoff product theorem implies the axiom of choice
• On the Cartesian Product of Two Compact Spaces
• The axiom of choice
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