论文标题
连续无非块点
Continuum Without Non-Block Points
论文作者
论文摘要
对于任何组合$ e \ subset \ mathbb h^*$和对应的近乎固定类$ \ mathscr e \ subsetω^*$，我们证明以下是等效的：（1）$ e $适当地包含一个密集的semicontinuum。 （2）$ e $的每个可计数子集都包含在$ e $的密集的适当的半theminuum中。 （3）$ e $的每个可计数子集与$ e $的某些密集的半themintinuum脱节。 （4）$ \ Mathscr e $在有限的超滤器单调顺序中具有最小的元素。 （5）$ \ mathscr e $具有$ q $ - 点。结果是NCF等同于$ \ Mathbb H^*$，其中没有适当的密度半tiNuum，也没有非块点。这给出了对作者问题的公理答案。因此，每个已知的连续体在每个点都有一个适当的密集半牙周，要么无点。我们检查了不可分解的连续体的结构，而这种连续性的失败，并推断出它们包含具有密集内部的最大半神经。
For any composant $E \subset \mathbb H^*$ and corresponding near-coherence class $\mathscr E \subset ω^*$ we prove the following are equivalent : (1) $E$ properly contains a dense semicontinuum. (2) Each countable subset of $E$ is contained in a dense proper semicontinuum of $E$. (3) Each countable subset of $E$ is disjoint from some dense proper semicontinuum of $E$. (4) $\mathscr E $ has a minimal element in the finite-to-one monotone order of ultrafilters. (5) $\mathscr E $ has a $Q$-point. A consequence is that NCF is equivalent to $\mathbb H^*$ containing no proper dense semicontinuum and no non-block points. This gives an axiom-contingent answer to a question of the author. Thus every known continuum has either a proper dense semicontinuum at every point or at no points. We examine the structure of indecomposable continua for which this fails, and deduce they contain a maximum semicontinuum with dense interior.
