4 problems

Let $({\mathcal M},\rho)$ be a pseudometric space, let $X$ be a Banach space, and let $m$ be a fixed positive integer. Set … For a set-valued mapping…

Let $C^{k,\omega }({\bf R}^{n})$ be the space of functions on ${\bf R}^{n}$ with $k$ derivatives whose $k$th-order derivatives have modulus of continuity controlled by $\omega$. It…

Stabilization conjecture. There exist $\ell+1$ numbers $\lambda_1,\ldots,\lambda_{\ell+1}\ge1$ such that, for every $F$ satisfying the finiteness-principle hypothesis that each res…

The stabilization conjecture. There exists a sequence $\vec{\lambda}=\{\lambda_k:1\le k\le\ell+1\}$ with every $\lambda_k\ge1$ such that, for every set-valued mapping…