4 problems

Feng–Huang–Rao's conjecture. If, for some $i\in I$, $\log\alpha_i\notin\operatorname{span}_{\mathbb{Q}}\\{\log\beta_j\\}_{j\in J}$, then

Let $E,F\subset\mathbb{R}^d$ be two totally disconnected non-trivial self-similar sets, generated by iterated function systems $\Phi=\{\varphi_i\}_{i\in I}$ and…

Let $F$ and $E$ be totally disconnected self-similar sets in $\mathbb{R}^d$, generated by the iterated function systems $\Phi=\lbrace\phi_i\rbrace_{i=1}^l$ and…

Let $\Phi=\{\phi_i(x)=\alpha_i x+a_i\}_{i=1}^m$ and $\Psi=\{\psi_j(x)=\beta_jx+b_j\}_{j=1}^{\ell}$ be self-similar iterated function systems on $\mathbb R$, with attractors…