Lindelöf property and the iterated continuous function spaces
Volume 143 / 1993
Fundamenta Mathematicae 143 (1993), 87-95
DOI: 10.4064/fm-143-1-87-95
Abstract
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.
