Perfect independent sets with respect to infinitely many relations
arXiv:1510.05127
Abstract
We prove a result on perfect cliques with respect to countably many G-delta relations on a complete metric space. As an application, we show that a Polish group contains a free subgroup generated by a perfect set as long as it contains any uncountable free subgroup. This answers a recent question of Głcab and Strobin.
10 pages