7 problems

Let $C_1$ and $C_2$ be Cantor sets in $\mathbb R$ with Lebesgue measure zero. Palis hypothesis. The arithmetic sum or difference $C_1\mathbin{+}C_2$ or $C_1\mathbin{-}C_2$ is eithe…

Let $(x_n)$ be a fast convergent sequence, and let $\widehat{E(x_n)}$ denote its adjoint Cantorval. An adjoint Cantorval is achievable if it is the achievement set of some converge…

Let $M$ denote an M-Cantorval, and say that an achievement set is of type $M\times M$ when it is a finite union of sets homeomorphic to $M\times M$. A cut of a set is understood in…

An achievement set in the plane is a set of the form … where the vector series is absolutely convergent. The source refers to a particular family of such planar achievement sets an…

For $p,q\in(0,1)$, define the achievement set … The question is the topological type of this set when $p>q>\frac12$. Cantor-set conjecture. $E(p^n,q^n)$ is a Cantor set for every…

Let $(x_n)$ be a real sequence in the absolutely summable space $\ell_1$, and let $c_{00}$ denote the space of sequences with only finitely many nonzero terms. For a sequence…

Let $X$ be a Cantor set and let $Y$ and $Z$ be Cantorvals satisfying … A set is an achievement set if it is the set of all subsums of an absolutely summable sequence. Achievement-s…