On the Compactness and Countable Compactness of $2^{ℝ}$ in ZF

Kyriakos Keremedis; Evangelos Felouzis; Eleftherios Tachtsis

On the Compactness and Countable Compactness of

2^{ℝ}

in ZF

Kyriakos Keremedis ; Evangelos Felouzis ; Eleftherios Tachtsis

Bulletin of the Polish Academy of Sciences. Mathematics, Tome 55 (2007), p. 293-302 / Harvested from The Polish Digital Mathematics Library

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Résumé

In the framework of ZF (Zermelo-Fraenkel set theory without the Axiom of Choice) we provide topological and Boolean-algebraic characterizations of the statements " $2^{ℝ}$ is countably compact" and " $2^{ℝ}$ is compact"

Publié le : 2007-01-01

Zbl 1134.03027

EUDML-ID : urn:eudml:doc:281197

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     author = {Kyriakos Keremedis and Evangelos Felouzis and Eleftherios Tachtsis},
     title = {On the Compactness and Countable Compactness of $2^{$\mathbb{R}$}$ in ZF},
     journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
     volume = {55},
     year = {2007},
     pages = {293-302},
     zbl = {1134.03027},
     language = {en},
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Kyriakos Keremedis; Evangelos Felouzis; Eleftherios Tachtsis. On the Compactness and Countable Compactness of $2^{ℝ}$ in ZF. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 55 (2007) pp. 293-302. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba55-4-1/