5 problems

Let $\mathbb K$ be a DC structure, and let its open core be the structure whose definable sets are generated by the open definable subsets of $\mathbb K^n$. The i-minimal open-core…

Let $C\subseteq\mathbb K^m$ be a $\mathcal D_\Sigma$ set, and let $f:C\to\mathbb K^n$ be definable, without assuming that $f$ is continuous. The dimension-image conjecture. One has…

Let $\mathbb K$ be restrained. A dimension function is a function $d$ assigning to every definable set a number in $\mathbb N\cup\{-\infty\}$ and satisfying the following axioms fo…

A restrained structure is a DC expansion of an ordered field such that, for every definable discrete set $D \subseteq \mathbb K^n$ and every definable function $g:D\to\mathbb K$, t…

Pigeonhole principle. If $f$ is injective, then it is surjective.