2 problems

Let $\mathcal R$ be a d-minimal expansion of $\bar{\mathbb{R}}$. Let $X \subseteq \mathbb{R}^n$ be a manifold definable in $\mathcal R$, and let $Y \subseteq X$ be clopen in $X$. C…

Let $\mathbb{K}$ be a structure in the setting of the paper, and let $X \subseteq \mathbb{K}^n$ be definable and closed. Definable Baire conjecture. The set $X$ is definably Baire.…