2 problems

Let $X$ be a compact Hausdorff space with a continuous free action of a nontrivial compact Hausdorff group $G$. Let $X*G$ denote the join equipped with the diagonal action of $G$.…

Let $G$ be a connected locally compact Hausdorff group acting continuously on a paracompact topological space $X$. The action is Palais-proper when it is a Cartan action and the or…