Every Lindel\"of scattered subspace of a $\Sigma$-product of real lines is $\sigma$-compact

Antonio Avilés; Mikołaj Krupski

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arXiv · 2411.10035

Every Lindel\"of scattered subspace of a $\Sigma$-product of real lines is $\sigma$-compact

Antonio Avilés·Mikołaj Krupski

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Abstract

We prove that every Lindel\"of scattered subspace of a $\Sigma$-product of first-countable spaces is $\sigma$-compact. In particular, we obtain the result stated in the title. This answers some questions of Tkachuk from [Houston J. Math. 48 (2022), no. 1, 171--181].

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Antonio Avilés, Mikołaj Krupski. 2024-11-15. Every Lindel\"of scattered subspace of a $\Sigma$-product of real lines is $\sigma$-compact. https://arxiv.org/abs/2411.10035

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