On cardinal sequences of scattered spaces

AbstractIt was proved by Dow and Simon that there are 2ω1 (as many as possible) pairwise nonhomeomorphic compact, T2, scattered spaces of height ω1 and width ω. In this paper, we prove that if α is an ordinal withω1 ⩽ α < ω2 and θ = 〈κξ: ξ < α〉 is a sequence of cardinals such that either κξ = ω or κξ = ω1 for every ξ < α, then there are 2ω1 pairwise nonhomeomorphic compact, T2, scattered spaces whose cardinal sequence is θ