Singular precalibers for topological products

DOI10.1016/J.TOPOL.2022.108190arXiv2207.02444WikidataQ114127898 ScholiaQ114127898MaRDI QIDQ6404115

Alejandro Ríos Herrejón

Publication date: 6 July 2022

Abstract: In this paper we prove that if $kappa$ is a singular cardinal with uncountable cofinality, then every power of a given topological space with precaliber $kappa$ has precaliber $kappa$ as well. Furthermore, if $X_{a}lpha:alpha<lambda$ is a family of topological spaces with precaliber $kappa$ and $lambda<cf(kappa)$, then $kappa$ is a precaliber for the topological product $prod{X}_{a}lpha:alpha<lambda$.

Mathematics Subject Classification ID

Cardinality properties (cardinal functions and inequalities, discrete subsets) (54A25) Product spaces in general topology (54B10) Applications of set theory (03E75) Other combinatorial set theory (03E05)

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