Israel Journal of Mathematics

, Volume 225, Issue 1, pp 427–449 | Cite as

Scattered spaces from weak diamonds

  • Miguel Ángel Gaspar-Arreola
  • Fernando Hernández-Hernández
  • Michael Hrušák


Parametrized ♦-principles introduced in [16] associated to the cardinal invariants s and b are used to construct (1) a family of sequentially compact spaces whose product is not countably compact — an example for the Scarborough–Stone problem, (2) a Jakovlev space, and (3) a compact sequential space of sequential order ω1. All spaces constructed are scattered, locally compact and of size ω1.


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Copyright information

© Hebrew University of Jerusalem 2018

Authors and Affiliations

  • Miguel Ángel Gaspar-Arreola
    • 1
  • Fernando Hernández-Hernández
    • 2
  • Michael Hrušák
    • 3
  1. 1.Universidad Aeronáutica en Querétaro, Carretera Estatal 200 QuerétaroColón, QuerétaroMéxico
  2. 2.Facultad de Ciencias Físico Matemáticas, UMSNHMorelia, MichoacánMéxico
  3. 3.Centro de Ciencas MatemáticasMorelia, MichoacánMéxico

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