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Scattered spaces from weak diamonds

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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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Authors and Affiliations

  1. Universidad Aeronáutica en Querétaro, Carretera Estatal 200 Querétaro, Tequisquiapan No. 22154 C.P. 76270, Colón, Querétaro, México

    Miguel Ángel Gaspar-Arreola

  2. Facultad de Ciencias Físico Matemáticas, UMSNH, Morelia, Michoacán, 58089, México

    Fernando Hernández-Hernández

  3. Centro de Ciencas Matemáticas, UNAM A.P. 61-3, Xangari, Morelia, Michoacán, 58089, México

    Michael Hrušák

Authors
  1. Miguel Ángel Gaspar-Arreola
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  2. Fernando Hernández-Hernández
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  3. Michael Hrušák
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Corresponding author

Correspondence to Miguel Ángel Gaspar-Arreola.

Additional information

The first author was supported by CONACyT scholarship 320304.

The second author was supported by CONACyT, grant 169078-F.

The third author gratefully acknowledges support from a PAPIIT grant IN 108014 and CONACyT grant 177758.

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Gaspar-Arreola, M.Á., Hernández-Hernández, F. & Hrušák, M. Scattered spaces from weak diamonds. Isr. J. Math. 225, 427–449 (2018). https://doi.org/10.1007/s11856-018-1669-1

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  • DOI: https://doi.org/10.1007/s11856-018-1669-1

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