4 problems

Let $E:\mathbf{BornCoarse}\to\mathbf{C}$ be a coarse homology theory, let $X$ be a uniform bornological coarse space, and let $i_\alpha:M_\alpha\to M$ be the canonical inclusions a…

Let $Y$ be a compact Hausdorff space and let $(Y_i)_{i\in\mathbb{N}}$ be a decreasing family of closed subspaces, with intersection given the subspace topology. Let…

Let $(X,d)$ be a proper metric space and let $n\in\mathbb{N}_0$. Let $H\mathcal{X}_*(X)$ denote coarse homology. Coarse Hurewicz conjecture. There is a natural morphism … that make…

Coarse mapping-space conjecture. The coarse homotopy group $\pi_n^c(X,\omega)$ is isomorphic to the group, or pointed set when appropriate, of base-ray-preserving coarse homotopy c…