In other words still, the function $ \begin{array}{ccc} { \text{linear maps } V \to W } & \ \to \ & { \text{functions } S \to W } \ \bar{f} &\mapsto &\bar{f} \circ i \end{array} $ is bijective. \end{iexample} Example: Given a set $ S $ , we can build a topological space $ D(S) $ by equipping $ S $ with the discrete topology: all subsets are open. With this topology, any map from $ S $ to a space $ X $ is continuous.