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Keywords:
function spaces; Corson-compact spaces; elementary substructures
function spaces; Corson-compact spaces; elementary substructures
Summary:
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 Lindelöf space of cardinality $\tau $ with one non-isolated point. This answers a question of Archangelskij [2].
References:
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