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 y∊ A, f(y) is a nonempty subset of y and ∣ f(y) ∣ = א₀) of Howard and Rubin are equivalent.
Publié le : 2003-07-14
Classification:
weak forms of the axiom of choice,
compactness,
sequential compactness,
Tychonoff product,
54D30,
54D55,
54D20
@article{1091030855,
author = {Keremedis, Kyriakos and Tachtsis, Eleftherios},
title = {On Sequentially Compact Subspaces of without the Axiom of Choice},
journal = {Notre Dame J. Formal Logic},
volume = {44},
number = {1},
year = {2003},
pages = { 175-184},
language = {en},
url = {http://dml.mathdoc.fr/item/1091030855}
}
Keremedis, Kyriakos; Tachtsis, Eleftherios. On Sequentially Compact Subspaces of without the Axiom of Choice. Notre Dame J. Formal Logic, Tome 44 (2003) no. 1, pp. 175-184. http://gdmltest.u-ga.fr/item/1091030855/