Measurable cardinals and fundamental groups of compact spaces
Volume 192 / 2006
Fundamenta Mathematicae 192 (2006), 87-92
MSC: Primary 03E55; Secondary 55Qxx.
DOI: 10.4064/fm192-1-6
Abstract
We prove that all groups can be realized as fundamental groups of compact spaces if and only if no measurable cardinals exist. If the cardinality of a group $G$ is nonmeasurable then the compact space $K$ such that $G=\pi _1K$ may be chosen so that it is path connected.
