Measurable cardinals and fundamental groups of compact spaces

Volume 192 / 2006

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


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.


  • Adam Prze/xdzieckiInstitute of Mathematics
    Warsaw University
    Banacha 2
    02-097 Warszawa, Poland

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