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In this article we prove that every isometric copy of C(L) in C(K) iscomplemented if L is compact Hausdorff of finite height and K is a compactHausdorff space satisfying the extension property, i.e., every closed subset ofK admits an extension operator. The space C(L) can be replaced by its subspaceC(L|F) consisting of functions that vanish on a closed subset F of L. We alsostudy the class of spaces having the extension property, establishing someclosure results for this class and relating it to other classes of compactspaces.

Extension property and complementation of isometric copies of continuous functions spaces