We apply elementary substructures to characterize the space Cp(X) for Corsoncompact spaces. As a result, we prove that a compact space X is Corson-compact, if Cp(X) can be represented as a continuous image of a closed subspace of (Lτ ) × Z, where Z is compact and Lτ denotes the canonical Lindelöf space of cardinality τ with one non-isolated point. This answers a question of Archangelskij [2].
