Small Valdivia compact spaces

We prove a preservation theorem for the class of Valdivia compact spaces, which involves inverse sequences of retractions of a certain kind. Consequently, a compact space of weight ⩽ ℵ 1 is Valdivia compact iff it is the limit of an inverse sequence of metric compacta whose bonding maps are retractions. As a corollary, we show that the class of Valdivia compacta of weight ⩽ ℵ 1 is preserved both under retractions and under open 0-dimensional images. Finally, we characterize the class of all Valdivia compacta in the language of category theory, which implies that this class is preserved under all continuous weight preserving functors.