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Title: Products of topological spaces and families of filters (English)
Author: Lipparini, Paolo
Language: English
Journal: Commentationes Mathematicae Universitatis Carolinae
ISSN: 0010-2628 (print)
ISSN: 1213-7243 (online)
Volume: 64
Issue: 3
Year: 2023
Pages: 373-394
Summary lang: English
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Category: math
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Summary: 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. (English)
Keyword: filter convergence
Keyword: ultrafilter
Keyword: product
Keyword: subproduct
Keyword: sequential compactness
Keyword: sequencewise $\mathcal P$-compactness
Keyword: Lindelöf property
Keyword: final $\lambda$-compactness
Keyword: $[ \mu, \lambda ]$-compactness
Keyword: Menger property
Keyword: Rothberger property
MSC: 54A20
MSC: 54B10
MSC: 54D20
idZBL: Zbl 07830515
idMR: MR4717508
DOI: 10.14712/1213-7243.2024.005
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Date available: 2024-03-18T10:47:28Z
Last updated: 2024-08-02
Stable URL: http://hdl.handle.net/10338.dmlcz/152305
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