A continuum without non-block points

作者：Anderson Daron^*

来源：Topology and Its Applications, 2017, 218: 42-52.

DOI：10.1016/j.topol.2016.12.014

• Continuum
• Shore point
• Non-block point
• Indecomposable continuum
• One composant
• Stone-Oech remainder
• H*
• Ultrafilter
• Q-point
• NCF
• omega*

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

• 出版日期2017-3-1