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We give an example of a compact space X whose iterated continuous function spaces Cₚ(X), CₚCₚ(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
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Gennady A. Sokolov (1993) studied this question.
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