发表机构
Czech Academy of Sciences; Jagiellonian University（捷克科学院; 雅盖隆大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
在ZFC中构造零维Tychonoff空间，使局部π-特征呈现ω<ω₁<ω₂的严格递增，且不依赖递减基的定义方式，结合星形与矩阵滤波器实现。
AI 中文摘要
我们在ZFC中回答了N. Carlson的一个问题，通过构造一个零维的Tychonoff空间$X$，该空间恰好有一个非孤立点，使得每个点都有一个递减的局部$\pi$-基，并且 \\[ \pi\chi(X)=\pi\chi_{\mathrm l}(X)=\omega <\pi\chi_{\mathrm c}(X)=\omega_1 <\pi\chi_{\mathrm d}(X)=\omega_2. \\] 一个预备的链细化引理表明，集合的子集的每个包含链都有一个反向良序的共初始子链，其基数受控。因此，该结果不依赖于递减局部$\pi$-基被理解为包含链、严格递减的超限序列还是弱递减的超限序列。该构造结合了一个可数星形滤波器（其中心局部$\pi$-特征至少为伪交集数$\mathfrak p$）和一个矩阵滤波器，后者给出了精确值$\omega_1$和$\omega_2$。
英文摘要
We answer in ZFC a question of N. Carlson by constructing a zero-dimensional Tychonoff space $X$, with exactly one non-isolated point, for which every point admits a decreasing local $π$-base and \[ πχ(X)=πχ_{\mathrm l}(X)=ω<πχ_{\mathrm c}(X)=ω_1 <πχ_{\mathrm d}(X)=ω_2. \] A preliminary chain-refinement lemma shows that every inclusion-chain of subsets of a set has a reverse-well-ordered coinitial subchain of controlled cardinality. Thus the result is independent of whether a decreasing local $π$-base is understood as an inclusion-chain, a strictly decreasing transfinite sequence, or a weakly decreasing transfinite sequence. The construction combines a countable star filter, whose centred local $π$-character is at least the pseudointersection number $\mathfrak p$, with a matrix filter that gives the exact values $ω_1$ and $ω_2$.
Comments10 pp., accepted for publication in Topology and its Applications
