Abstract This is a survey of four problems that are “classics” in many different senses of the word, and of several related problems associated with each one. The numbering of the Classic Problems picks up where that of a similar article left off about four decades ago: IX. Is every point of ω ⁎ a butterfly point? X. Is there a nonmetrizable perfectly normal, locally connected continuum? XI. Is there a normal space with a σ-disjoint base that is not paracompact? XII. Is there a regular symmetrizable space with a non- G δ point? Several related problems are given for each classic problem. Consistency results are summarized, and there is a discussion of each problem that explains various implications among the related problems and justifies calling certain problems equivalent. For each classic problem, an appendix goes deeper into some implications and/or includes reminisces. There is a purely set-theoretic problem related to Classic Problem IX. Call a filter on a set D nowhere maximal if it does not trace an ultrafilter on any subset of D. Related Problem D. Is every free ultrafilter the join of two nowhere maximal filters? It is shown that the special case of ultrafilters on ω is actually equivalent to Classic Problem IX.

中文翻译：

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经典问题 III

摘要 这是对四个在许多不同意义上的“经典”问题的调查，以及与每个问题相关的几个相关问题。经典问题的编号从大约四年前一篇类似文章的编号开始：IX。ω ⁎ 的每一点都是蝴蝶点吗？X. 是否存在不可计量的完全正规的、局部连接的连续统？十一。是否存在具有非超紧致基的 σ 不相交基的正规空间？十二. 是否存在具有非 G δ 点的正则对称空间？每个经典问题都给出了几个相关的问题。对一致性结果进行了总结，并对每个问题进行了讨论，解释了相关问题之间的各种含义，并证明了将某些问题称为等效的理由。对于每个经典问题，附录更深入地探讨了某些含义和/或包括回忆。有一个与经典问题 IX 相关的纯集合论问题。如果在 D 的任何子集上都没有跟踪超滤器，则在集合 D 上调用过滤器为无处极大值。相关问题 D. 每个自由超滤器是否都是两个无处极大值过滤器的连接？结果表明，ω 上的超滤波器的特殊情况实际上等价于经典问题 IX。