Every Lindelöf scattered subspace of a Σ-product of real lines is σ-compact

2024/11/15 by Avilés, Antonio, Krupski, Mikołaj
#54B10 #54D20 #54D45 #54G12 #FOS: Mathematics #General Topology (math.GN)

paper · doi:10.48550/arxiv.2411.10035

Abstract

We prove that every Lindelöf scattered subspace of a Σ-product of first-countable spaces is σ-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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