A density-functional theory for the wetting of an inert spherical-shell substrate by a single-component bull; vapor is developed, on the basis of the usual assumption that the pairwise intermolecular interaction is divided into a repulsive hard sphere and a weak attractive part. The substrate vapor-molecule pairwise interaction is also divided into a hard-wall repulsive interaction and a weak attractive tail. Choosing the attractive interactions properly, a second-order nonlinear functional differential equation results, which is solved numerically with appropriate boundary conditions. It is shown that the wetting layer, formed on the adsorbent, is either a thin or a thick film of finite thickness. Furthermore, in some cases the substrate is not at all wet. The wall-vapor and other interfacial tensions, the associated radii, and the principal tensors (the transverse p(T)(r) and normal p(N)(r)) are also calculated. The wall-vapor interface is mainly under tension (p(N)(r) > p(T)(r)).