Remarks on the Stone Spaces of the Integers and the Reals without AC
Horst Herrlich ; Kyriakos Keremedis ; Eleftherios Tachtsis
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 59 (2011), p. 101-114 / Harvested from The Polish Digital Mathematics Library
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In ZF, i.e., the Zermelo-Fraenkel set theory minus the Axiom of Choice AC, we investigate the relationship between the Tychonoff product 2(X), where 2 is 2 = 0,1 with the discrete topology, and the Stone space S(X) of the Boolean algebra of all subsets of X, where X = ω,ℝ. We also study the possible placement of well-known topological statements which concern the cited spaces in the hierarchy of weak choice principles.

Publié le : 2011-01-01
EUDML-ID : urn:eudml:doc:286175 
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     title = {Remarks on the Stone Spaces of the Integers and the Reals without AC},
     journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
     volume = {59},
     year = {2011},
     pages = {101-114},
     zbl = {1242.03072},
     language = {en},
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Horst Herrlich; Kyriakos Keremedis; Eleftherios Tachtsis. Remarks on the Stone Spaces of the Integers and the Reals without AC. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 59 (2011) pp. 101-114. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba59-2-1/