# Wydawnictwa / Czasopisma IMPAN / Fundamenta Mathematicae / Wszystkie zeszyty

## Measurable cardinals and fundamental groups of compact spaces

### Tom 192 / 2006

Fundamenta Mathematicae 192 (2006), 87-92 MSC: Primary 03E55; Secondary 55Qxx. DOI: 10.4064/fm192-1-6

#### Streszczenie

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.