Geodesic
Lindelöf property and the iterated continuous function spaces
Fundamenta Mathematicae, Tome 143 (1993) no. 1, pp. 87-95
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We give an example of a compact space X whose iterated continuous function spaces $C_{p}(X)$, $C_pC_p(X), ...$ are Lindelöf, but X is not a Corson compactum. This solves a problem of Gul'ko (Problem 1052 in [11]). We also provide a theorem concerning the Lindelöf property in the function spaces $C_{p}(X)$ on compact scattered spaces with the $ω_1$th derived set empty, improving some earlier results of Pol [12] in this direction. 
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G. Sokolov. Lindelöf property and the iterated continuous function spaces. Fundamenta Mathematicae, Tome 143 (1993) no. 1, pp. 87-95. doi: 10.4064/fm-143-1-87-95

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