Article
| 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 |
| DOI: | 10.14712/1213-7243.2024.005 |
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| Date available: | 2024-03-18T10:47:28Z |
| Last updated: | 2024-03-18 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/152305 |
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