2 problems

Let $X$ and $Y$ be compact metric spaces with finite shape dimension, let $\mathfrak{a}:cX\to cY$ be a coarse map, and suppose that $M_X$ has $t\in\mathbb{N}$ ends. Choose…

Let $M$ be a closed aspherical manifold of dimension greater than $1$, and let $\widetilde{M}$ denote its universal cover. A space is strongly connected at infinity when its end ha…