Embedding of a T0 space into a power of the Sierpiński space ($X\hookrightarrow S^{\mathbf{Top}(X,S)}$)

For a T0 space $X$, evaluation against all continuous maps $g:X\to S$ is a homeomorphism onto its image under the mapinto a power of the Sierpiński space. The $T_0$ axiom makes it injective, and the coordinate inverse images of $\{1\}$ recover every open subset of $X$.