Strong Fréchet properties of spaces constructed from squares and AD families

William Chen-Mertens; César Corral-Rojas; Paul J. Szeptycki

doi:10.4995/agt.2023.18504

Strong Fréchet properties of spaces constructed from squares and AD families

William Chen-Mertens, César Corral-Rojas, Paul J. Szeptycki

Research output: Contribution to journal › Article › peer-review

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 bise-quential. 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.

Original language	English
Pages (from-to)	379-389
Number of pages	11
Journal	Applied General Topology
Volume	24
Issue number	2
DOIs	https://doi.org/10.4995/agt.2023.18504
State	Published - 2 Oct 2023
Externally published	Yes

Keywords

bi-sequential
Fréchet-Urysohn
w-space
W-space
α-space

ASJC Scopus subject areas

Geometry and Topology

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10.4995/agt.2023.18504

Cite this

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abstract = "We answer questions of Arhangel{\textquoteright}skiĭ using spaces defined from combinatorial objects. We first establish further convergence properties of a space constructed from ✷(κ) showing it is Fr{\'e}chet-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 Fr{\'e}chet α1 space that is not bise-quential. In addition, if we do not require the space being α1, we can construct a ZFC example of a countable absolutely Fr{\'e}chet space that is not bisequential from an almost disjoint family of subsets of the natural numbers.",

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N2 - 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 bise-quential. 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.

AB - 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 bise-quential. 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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Strong Fréchet properties of spaces constructed from squares and AD families

Abstract

Keywords

ASJC Scopus subject areas

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