2 problems

Let $G$ be a countable group. Write $\operatorname{CO}(G)$ for the space of circular orders on $G$, and let $\operatorname{Hom}(G,\operatorname{Homeo}_+(S^1))$ be the space of acti…

Free-product no-isolated-points conjecture. The space $\operatorname{CO}(G*H)$ either has no isolated points or is finite. In particular, if it is infinite, then…