A note on monolithic scattered compacta

For a Banach space E, it is well-known that a necessary condition for E to have the controlled separable complementation property (CSCP, for short) is that the dual unit ball BE⁎ be monolithic in the weak-star topology. We prove here that when X is a scattered first countable locally compact space, then monolithicity of X turns out to be sufficient for C0(X) to enjoy the CSCP.