Strong Fréchet properties of spaces constructed from squares and AD families

• Chen-Mertens, William ^[1] ; Corral-Rojas, César ^[1] ; Szeptycki, Paul J. ^[1]
  1. [1] York University
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 24, Nº. 2, 2023, págs. 379-389
• Idioma: inglés
• DOI: 10.4995/agt.2023.18504
• Enlaces
  • Texto completo
• Resumen

  • We answer questions of Arhangel'skiĭ using spaces defined from combinatorial objects. We first establish further convergence properties of a space constructed from □ ( κ ) showing it is Fréchet-Urysohn for finite sets and a w-space that is not a W-space. We also show that under additional assumptions it may be not bi-sequential, and so providing a consistent example of an absolutely Fréchet α1 space that is not bisequential. In addition, if we do not require the space being α1, we can construct a ZFC example of a countable absolutely Fréchet space that is not bisequential from an almost disjoint family of subsets of the natural numbers.

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