Strong Fréchet properties of spaces constructed from squares and AD families




Fréchet-Urysoh, bi-sequential, α1-space, W-space, w-space


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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How to Cite

W. Chen-Mertens, C. Corral-Rojas, and P. J. Szeptycki, “Strong Fréchet properties of spaces constructed from squares and AD families”, Appl. Gen. Topol., vol. 24, no. 2, pp. 379–389, Oct. 2023.



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