3 problems

Local model conjecture. The pair $(\mathcal H(M),\mathcal H_c(M))$ is locally homeomorphic to $(\square^\omega l_2,\boxdot^\omega l_2)$ at the identity $\mathrm{id}_M$ of $M$. In p…

Let $\mathcal H^u(\mathbb R^n)_b$ denote the group of bounded uniform homeomorphisms of Euclidean space $\mathbb R^n$, equipped with the sup-metric, and let $\ell_\infty$ be the Ba…

Hurewicz-set translate conjecture. If $H\subset {\mathbb R}^{\mathbb N}$ is a Hurewicz set, then for each countable dimensional set $C\subset {\mathbb R}^{\mathbb N}$,