# Baire category theorem

The work shows that free groups admit amenable actions on unital simple AF-algebras, thereby settling for free groups the last remaining case of the existence problem for amenable actions of non-amenable groups on classifiable simple C*-algebras; the proof relies on the Baire category theorem, and the result was obtained with substantial assistance from GPT-6 Astra.

The work shows that free groups admit amenable actions on unital simple AF-algebras, thereby settling for free groups the last remaining case of the existence problem for amenable actions of non-amenable groups on classifiable simple C*-algebras; the proof relies on the Baire category theorem, and the result was obtained with substantial assistance from GPT-6 Astra.