The hyperspace of a compact space .1

We investigate the properties monolithic and d-separable for the hyperspace H(X) of all nonempty closed subsets of a compact Hausdorff space X. A. Arhangelskii has asked whether H(X) monolithic is equivalent to X metrizable. We answer this with: Let X be a compact orderable space. Then H(X) is monolithic iff X is monolithic and hereditarily Lindelof. So, a Suslin continuum has a monolithic hyperspace. In contrast, MA(omega(1)) implies that for any compact Hausdorff space X, H(X) is monolithic iff X is metrizable. We prove that H(X) is always d-separable. A special case of this yields that every locally compact Hausdorff space X has a discrete (in H(X)) pi-net.