4 problems

Let ${\mathcal A}$ be an analytic subset of a Polish space and let ${\mathcal Y}$ be separable metrizable. For a function $f:{\mathcal A}\to{\mathcal Y}$, interpret…

Let $m,n\in\omega$. For a class of Borel functions, $\mathbf{dec}_{n+1}\mathcal{F}$ denotes functions decomposable into countably many $\mathcal{F}$-functions with…

Let $X$ be an analytic space, $Y$ a separable metrizable space, $1<n<m<\omega$, and $f\in\Sigma_{m,n}(X,Y)$. Topology-refinement reformulation of the strong Jayne–Rogers conjecture…

Let $X$ and $Y$ be separable metrizable spaces with $X$ analytic, and let $\widetilde{Y}$ denote the completion used for the graph formulation. For $1<n<\omega$, let…