Remarks on the Stone Spaces of the Integers and the Reals without AC

Horst Herrlich, Kyriakos Keremedis, and Eleftherios Tachtsis. "Remarks on the Stone Spaces of the Integers and the Reals without AC." Bulletin of the Polish Academy of Sciences. Mathematics 59.2 (2011): 101-114. <http://eudml.org/doc/286175>.

@article{HorstHerrlich2011,
abstract = {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.},
author = {Horst Herrlich, Kyriakos Keremedis, Eleftherios Tachtsis},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
keywords = {axiom of choice; weak forms of AC; Stone spaces; Boolean prime ideal theorem; filters; ultrafilters; compactness; Loeb spaces},
language = {eng},
number = {2},
pages = {101-114},
title = {Remarks on the Stone Spaces of the Integers and the Reals without AC},
url = {http://eudml.org/doc/286175},
volume = {59},
year = {2011},
}

TY - JOUR
AU - Horst Herrlich
AU - Kyriakos Keremedis
AU - Eleftherios Tachtsis
TI - Remarks on the Stone Spaces of the Integers and the Reals without AC
JO - Bulletin of the Polish Academy of Sciences. Mathematics
PY - 2011
VL - 59
IS - 2
SP - 101
EP - 114
AB - 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.
LA - eng
KW - axiom of choice; weak forms of AC; Stone spaces; Boolean prime ideal theorem; filters; ultrafilters; compactness; Loeb spaces
UR - http://eudml.org/doc/286175
ER -