Abstract We establish that, for any Tychonoff space X, at least one of the function spaces C p C p ( X ) and C p C p C p ( X ) must have a dense subspace of countable pseudocharacter. If GCH holds, then at least one of the spaces C p ( X ) and C p C p ( X ) has a dense subspace of countable pseudocharacter. We also prove that all iterated function spaces C p , n ( K ) have a uniformly dense subspace of countable pseudocharacter whenever K is a Corson compact space. Our results solve several published open questions.

中文翻译：

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对于每个空间 X，CC(X) 或 CCC(X) 是 ψ-separable

摘要 我们确定，对于任何 Tychonoff 空间 X，函数空间 C p C p ( X ) 和 C p C p C p ( X ) 中的至少一个必须具有可数伪字符的稠密子空间。如果 GCH 成立，则空间 C p ( X ) 和 C p C p ( X ) 中的至少一个具有可数伪字符的稠密子空间。我们还证明，只要 K 是 Corson 紧空间，所有迭代函数空间 C p , n ( K ) 都具有可数伪字符的均匀稠密子空间。我们的结果解决了几个公开的公开问题。