Remarks on the Stone Spaces of the Integers and the Reals without
Tom 59 / 2011
Bulletin Polish Acad. Sci. Math. 59 (2011), 101-114
MSC: 03E25, 54B10, 54D30, 54D80.
DOI: 10.4064/ba59-2-1
Streszczenie
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.
