A continuum without non-block points

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• 作者：Daron Anderson ^{d.anderson2@nuigalway.ie}
• 关键词：54F15
• 刊名：Topology and its Applications
• 出版年：2017
• 出版时间：1 March 2017
• 年：2017
• 卷：218
• 期：Complete
• 页码：42-52
• 全文大小：354 K
• 卷排序：218

文摘

For any composant E⊂H⁎E⊂H⁎ and corresponding near-coherence-class E⊂ω⁎E⊂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) EE has a minimal element in the finite-to-one weakly-increasing order of ultrafilters. (5) EE has a Q  -point. A consequence is that NCF is equivalent to H⁎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.