Example 1

If $\mathfrak{S}$ is the set of all finite subsets of E, then the $\mathfrak{S}$-topology is the topology of simple convergence and the space $\mathscr{L}_{\mathfrak{S}}(E; F)$ is also denoted by $\mathscr{L}_s(E; F)$. A bounded subset of $\mathscr{L}_s(E; F)$ is called a simply bounded subset of $\mathscr{L}(E; F)$.