Example 2

If $\mathfrak{S}$ is the set of compact (resp. precompact, compact convex) subsets, then the $\mathfrak{S}$-topology is called the topology of compact (resp. precompact, compact convex) convergence and the space $\mathscr{L}_{\mathfrak{S}}(E; F)$ is also denoted by $\mathscr{L}_c(E; F)$ (resp. $\mathscr{L}_{pc}(E; F)$, $\mathscr{L}_{cc}(E; F)$). (Cf. IV, p. 48, exerc. 7.)