1. Strong Fréchet properties of spaces constructed from squares and AD families
- Author
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William Chen-Mertens, César Corral-Rojas, and Paul J. Szeptycki
- Subjects
fréchet-urysoh ,bi-sequential ,α1-space ,w-space ,Mathematics ,QA1-939 ,Analysis ,QA299.6-433 - Abstract
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.
- Published
- 2023
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