Geodesic
Products of topological spaces and families of filters
Commentationes Mathematicae Universitatis Carolinae, Tome 64 (2023) no. 3, pp. 373-394.

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We show that, under suitably general formulations, covering properties, accumulation properties and filter convergence are all equivalent notions. This general correspondence is exemplified in the study of products. We prove that a product is Lindelöf if and only if all subproducts by $\leq \omega_1 $ factors are Lindelöf. Parallel results are obtained for final $ \omega_n$-compactness, $[ \lambda, \mu ]$-compactness, the Menger and the Rothberger properties.
DOI : 10.14712/1213-7243.2024.005
Classification : 54A20, 54B10, 54D20
Keywords: filter convergence; ultrafilter; product; subproduct; sequential compactness; sequencewise $\mathcal P$-compactness; Lindelöf property; final $\lambda$-compactness; $[ \mu, \lambda ]$-compactness; Menger property; Rothberger property 
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Lipparini, Paolo. Products of topological spaces and families of filters. Commentationes Mathematicae Universitatis Carolinae, Tome 64 (2023) no. 3, pp. 373-394. doi : 10.14712/1213-7243.2024.005. http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2024.005/

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