Geodesic
Remarks on the Stone Spaces of the Integers and the Reals without ${\bf AC}$
Horst Herrlich 1   ; Kyriakos Keremedis 2   ; Eleftherios Tachtsis 3
1 Feldhäuser Str. 69 28865 Lilienthal, Germany
2 Department of Mathematics University of the Aegean Karlovassi, Samos 83200, Greece
3 Department of Statistics and Actuarial-Financial Mathematics University of the Aegean Karlovassi, Samos 83200, Greece
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 59 (2011) no. 2, pp. 101-114 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

Voir la notice de l'article

In $\mathbf{ZF}$, i.e., the Zermelo–Fraenkel set theory minus the Axiom of Choice $\mathbf{AC}$, we investigate the relationship between the Tychonoff product $\mathbf{2}^{\mathcal{P}(X)}$, where $\mathbf{2}$ is $2=\{0,1\}$ with the discrete topology, and the Stone space $S(X)$ of the Boolean algebra of all subsets of $X$, where $X=\omega,\mathbb{R}$. We also study the possible placement of well-known topological statements which concern the cited spaces in the hierarchy of weak choice principles.
DOI : 10.4064/ba59-2-1
Keywords: mathbf zermelo fraenkel set theory minus axiom choice mathbf investigate relationship between tychonoff product mathbf mathcal where mathbf discrete topology stone space boolean algebra subsets nbsp where omega mathbb study possible placement well known topological statements which concern cited spaces hierarchy weak choice principles

Horst Herrlich  1   ; Kyriakos Keremedis  2   ; Eleftherios Tachtsis  3

1 Feldhäuser Str. 69 28865 Lilienthal, Germany
2 Department of Mathematics University of the Aegean Karlovassi, Samos 83200, Greece
3 Department of Statistics and Actuarial-Financial Mathematics University of the Aegean Karlovassi, Samos 83200, Greece 
@article{10_4064_ba59_2_1,
     author = {Horst Herrlich and Kyriakos Keremedis and Eleftherios Tachtsis},
     title = {Remarks on the {Stone} {Spaces} of
the {Integers} and the {Reals} without ${\bf AC}$},
     journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
     pages = {101--114},
     year = {2011},
     volume = {59},
     number = {2},
     doi = {10.4064/ba59-2-1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/ba59-2-1/}
}
TY  - JOUR
AU  - Horst Herrlich
AU  - Kyriakos Keremedis
AU  - Eleftherios Tachtsis
TI  - Remarks on the Stone Spaces of
the Integers and the Reals without ${\bf AC}$
JO  - Bulletin of the Polish Academy of Sciences. Mathematics
PY  - 2011
SP  - 101
EP  - 114
VL  - 59
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4064/ba59-2-1/
DO  - 10.4064/ba59-2-1
LA  - en
ID  - 10_4064_ba59_2_1
ER  - 
%0 Journal Article
%A Horst Herrlich
%A Kyriakos Keremedis
%A Eleftherios Tachtsis
%T Remarks on the Stone Spaces of
the Integers and the Reals without ${\bf AC}$
%J Bulletin of the Polish Academy of Sciences. Mathematics
%D 2011
%P 101-114
%V 59
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4064/ba59-2-1/
%R 10.4064/ba59-2-1
%G en
%F 10_4064_ba59_2_1
Horst Herrlich; Kyriakos Keremedis; Eleftherios Tachtsis. Remarks on the Stone Spaces of
the Integers and the Reals without ${\bf AC}$. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 59 (2011) no. 2, pp. 101-114. doi: 10.4064/ba59-2-1

Cité par Sources :