8 problems

Let $N^n_m$ be the subset of $\mathbb{R}^n$ consisting of points with at most $m$ rational coordinates. Chigogidze's conjecture. Every $m$-dimensional subset of $\mathbb{R}^n$ can…

Let $N^n_m$ be the subset of $\mathbb{R}^n$ consisting of points with at most $m$ rational coordinates. When $n<2m+1$, call $N^n_m$ an unstable Nöbeling space. A boundary at infini…

Let an abstract $n$-dimensional Nöbeling manifold of weight $\kappa$ be an $n$-dimensional complete metric space of weight $\kappa$ that is an absolute neighborhood extensor in dim…

An $n$-dimensional Nöbeling space is a subset of $\mathbb{R}^{2n+1}$ consisting of points with at most $n$ rational coordinates. Nöbeling-space analogue conjecture. In the 1980s it…

Let $S$ be a $p$-punctured surface of genus $g$, and set $n=3g+p-4$. Define $k$ by $k=0$ if $g=0$, $k=g-1$ if both $p\neq 0$ and $g\neq 0$, and $k=g-2$ if $p=0$. Let…

Let $S$ be a finite-type hyperbolic surface and write $\mathcal{P} \mathcal{M} \mathcal{L} (S)$ for its projective measured lamination space. Suppose…

Let $S$ be a finite-type hyperbolic surface, and let $\mathcal{E} \mathcal{L} (S)$ denote its ending lamination space. An $m$-dimensional Nöbeling space is the subspace of…

Let $S_{g,p}$ be a surface of genus $g$ with $p$ punctures, and let … be its complexity. Let $\mathcal{EL}$ denote the space of ending laminations on $S_{g,p}$, equipped with its n…