Abstract:We apply elementary substructures to characterize the space $C_p(X)$ for Corson-compact spaces. As a result, we prove that a compact space $X$ is Corson-compact, if $C_p(X)$ can be represented as a continuous image of a closed subspace of $(L_{\tau })^{\omega }\times Z$, where $Z$ is compact and $L_{\tau }$ denotes the canonical Lindel\"of space of cardinality $\tau $ with one non-isolated point. This answers a question of Archangelskij [2].
Keywords: function spaces, Corson-compact spaces, elementary substructures
AMS Subject Classification: Primary 54C