Pointwise Topological Convergence and Topological Graph Convergence of Set-Valued Maps

Abstract

Let $X, Y$ be topological spaces and $\{F_n: n \in \omega\}$ be a sequence of set-valued maps from $X$ to $Y$ with the topological limit $G$ and with the graph limit $F$. We give an answer to the question from [Ko]: which conditions on $X, Y$ and/or $\{F, G, F_n: n \in \omega\}$ are needed to $F = G$.