Scattered spaces from weak diamonds

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

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 Querétaro - Tequisquiapan No. 22154 C.P.Colón, QuerétaroMéxico
  2. 2.Facultad de Ciencias Físico Matemáticas, UMSNH. MoreliaMichoacánMéxico
  3. 3.Centro de Ciencas Matemáticas, UNAM A.P. 61-3, Xangari, MoreliaMichoacánMéxico

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