8 problems

Let $\mathcal{T}_{\chi}$ and $\mathcal{T}_{\psi}$ be the tiling spaces associated with substitutions $\chi$ and $\psi$, and let $\tilde{\chi}$ and $\tilde{\psi}$ denote the associa…

Let $\mathcal{M}$ be the class of maps under consideration, let $\operatorname{invlim} f$ denote the inverse limit of $f$, let $\chi_f$ be the substitution associated with $f$, and…

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 $X$ be a ladder consisting of two rays joined at height $0$ and rungs of lengths $l_m\in\mathbb{N}$ at heights $h_m\in\mathbb{N}$, where $(h_m)$ is strictly increasing, and equ…

Polylogarithmic bound conjecture. There exists a polynomial $p$ such that the effective asymmetric coloring conjecture holds with

Effective asymmetric coloring conjecture. There exists a function $g:\mathscr{Gr}\to\mathbb N$ such that, whenever $k\geq g(G_0)$, the inverse limit of this system admits a zero-ne…

Let $f$ be an endomorphism, with inverse limit space $\overleftarrow M_f$ and natural extension $\overleftarrow f$. It is $C^1$-inverse limit stable if every $C^1$ perturbation…

A singular quotient $3$-manifold is a quotient space of a topological $3$-manifold by a continuum that generates a singular point. An inverse limit of closed $3$-manifolds is a spa…