On the Compactness and Countable Compactness of $2^{\mathbb{R}}$ in ZF
Volume 55 / 2007
Bulletin Polish Acad. Sci. Math. 55 (2007), 293-302
MSC: 03E25, 54A35, 54B10, 54D20, 54D30.
DOI: 10.4064/ba55-4-1
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 “$2^{\mathbb{R}}$ is countably compact” and “$2^{\mathbb{R}}$ is compact”
