The author considers injective Fréchet spaces (i.e. those which are complemented in every Fréchet space containing them), in particular the problem of classifying them. He shows that an injective Fréchet space of the form \(C(T)\) (the space of continuous functions on the locally compact space \(T\)) either contains a copy of a space of the form \(\prod_{i\in\mathbb{N}} \ell_ \infty(\Gamma_ i)\) (where the \(\Gamma_ i\) are uncountable) or it is a product \(\prod_{i\in\mathbb{N}}C(T_ i)\) corresponding to a splitting of \(T\) into the disjoint sum of compact and open subsets \(T_ i\).