4 problems

Let $D_j\subset\mathbb{C}^{n_j}$ be domains, let $A_j\subset D_j$ be locally pluriregular Borel sets for $j=1,\dots,N$, and let … Let $U\subset D_1\times\dots\times D_N$ be a conne…

Let $0<\xi<\omega_1$. For each such $\xi$, let $\mathbb{X}_\xi$ and $\mathbb{Y}_\xi$ be Polish spaces, and let…

Let $\Omega$ be an irreducible analytic set in a space of convergent power series, and let $f\in\Omega$. Define the algebraic tangent space by … and the geometric tangent space by…

Diederich–Pinchuk cluster-set conjecture. The cluster set $\operatorname{cl}(A_j)$ is not entirely contained in $N$. Although open in general, the conjecture was proved in dimensio…