4 problems

Let $X$ be a complete metric space, let $F\subseteq X$ be a nonempty closed set, and let $\{U_n\}_{n\in\omega}$ be a sequence of nonempty open sets in $X$ such that each $U_n$ is d…

Let $\mathbb{I}=[0,1]$, let $\mathcal{C}$ denote the family of bivariate copulas, and let $\mathcal{C}_{mcd}$ be the subclass of mutually completely dependent copulas. Let…

For a copula $C$, write $\partial_1C(x,y)$ for the partial derivative with respect to the first variable, when it exists. A subclass of copulas is called typical when it contains a…

For a family of periodic operators, let the dichotomy refer to the alternatives that the degeneracy locus is contained in a proper algebraic subset of parameter space or that degen…