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

Kyriakos Keremedis, Evangelos Felouzis, and Eleftherios Tachtsis. "On the Compactness and Countable Compactness of $2^{ℝ}$ in ZF." Bulletin of the Polish Academy of Sciences. Mathematics 55.4 (2007): 293-302. <http://eudml.org/doc/281197>.

@article{KyriakosKeremedis2007,
abstract = {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"},
author = {Kyriakos Keremedis, Evangelos Felouzis, Eleftherios Tachtsis},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
keywords = {axiom of choice; Tychonoff products; Tikhonov products; compact spaces; countably compact spaces; Lindelöf spaces; maximal clopen (open, closed, regular open) filters.},
language = {eng},
number = {4},
pages = {293-302},
title = {On the Compactness and Countable Compactness of $2^\{ℝ\}$ in ZF},
url = {http://eudml.org/doc/281197},
volume = {55},
year = {2007},
}

TY - JOUR
AU - Kyriakos Keremedis
AU - Evangelos Felouzis
AU - Eleftherios Tachtsis
TI - On the Compactness and Countable Compactness of $2^{ℝ}$ in ZF
JO - Bulletin of the Polish Academy of Sciences. Mathematics
PY - 2007
VL - 55
IS - 4
SP - 293
EP - 302
AB - 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"
LA - eng
KW - axiom of choice; Tychonoff products; Tikhonov products; compact spaces; countably compact spaces; Lindelöf spaces; maximal clopen (open, closed, regular open) filters.
UR - http://eudml.org/doc/281197
ER -