Definition 3.1.9 (Generated Topology).label Let $X$ be a topological space and $\s\suf\cali{P}(X)$ then $X$ is $\s$-generated if the topology on $X$ is the final topology generated by the inclusion maps $\curl{\iota_S:S\to X:S\in\s}$. If $\kappa\suf \cali{P}(X)$ is the collection of precompact sets of $X$ and $X$ is $\kappa$-generated then $X$ is compactly generated.