Products of topological spaces and families of filters

Paolo Lipparini

Commentationes Mathematicae Universitatis Carolinae (2023)

  • Volume: 64, Issue: 3, page 373-394
  • ISSN: 0010-2628

Abstract

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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 ≤ ω 1 factors are Lindelöf. Parallel results are obtained for final ω n -compactness, [ λ , μ ] -compactness, the Menger and the Rothberger properties.

How to cite

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Lipparini, Paolo. "Products of topological spaces and families of filters." Commentationes Mathematicae Universitatis Carolinae 64.3 (2023): 373-394. <http://eudml.org/doc/299236>.

@article{Lipparini2023,
abstract = {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 $\le \omega _1 $ factors are Lindelöf. Parallel results are obtained for final $ \omega _n$-compactness, $[ \lambda , \mu ]$-compactness, the Menger and the Rothberger properties.},
author = {Lipparini, Paolo},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {filter convergence; ultrafilter; product; subproduct; sequential compactness; sequencewise $\mathcal \{P\}$-compactness; Lindelöf property; final $\lambda $-compactness; $[ \mu , \lambda ]$-compactness; Menger property; Rothberger property},
language = {eng},
number = {3},
pages = {373-394},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Products of topological spaces and families of filters},
url = {http://eudml.org/doc/299236},
volume = {64},
year = {2023},
}

TY - JOUR
AU - Lipparini, Paolo
TI - Products of topological spaces and families of filters
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2023
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 64
IS - 3
SP - 373
EP - 394
AB - 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 $\le \omega _1 $ factors are Lindelöf. Parallel results are obtained for final $ \omega _n$-compactness, $[ \lambda , \mu ]$-compactness, the Menger and the Rothberger properties.
LA - eng
KW - filter convergence; ultrafilter; product; subproduct; sequential compactness; sequencewise $\mathcal {P}$-compactness; Lindelöf property; final $\lambda $-compactness; $[ \mu , \lambda ]$-compactness; Menger property; Rothberger property
UR - http://eudml.org/doc/299236
ER -

References

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