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2003 On Sequentially Compact Subspaces of 𝕉 without the Axiom of Choice
Kyriakos Keremedis, Eleftherios Tachtsis
Notre Dame J. Formal Logic 44(3): 175-184 (2003). DOI: 10.1305/ndjfl/1091030855


We show that the property of sequential compactness for subspaces of 𝕉 is countably productive in ZF. Also, in the language of weak choice principles, we give a list of characterizations of the topological statement 'sequentially compact subspaces of 𝕉 are compact'. Furthermore, we show that forms 152 (= every non-well-orderable set is the union of a pairwise disjoint well-orderable family of denumerable sets) and 214 (= for every family A of infinite sets there is a function f such that for all yA, f(y) is a nonempty subset of y and ∣ f(y) ∣ = א₀) of Howard and Rubin are equivalent.


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Kyriakos Keremedis. Eleftherios Tachtsis. "On Sequentially Compact Subspaces of 𝕉 without the Axiom of Choice." Notre Dame J. Formal Logic 44 (3) 175 - 184, 2003.


Published: 2003
First available in Project Euclid: 28 July 2004

zbMATH: 1071.03035
MathSciNet: MR2130789
Digital Object Identifier: 10.1305/ndjfl/1091030855

Primary: 54D20 , 54D30 , 54D55

Keywords: compactness , Sequential compactness , Tychonoff product , weak forms of the axiom of choice

Rights: Copyright © 2003 University of Notre Dame

Vol.44 • No. 3 • 2003
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