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 Lindelof if and only if all subproducts by <= omega(1) factors are Lindelof. Parallel results are obtained for final omega(n)-compactness, [lambda, mu]-compactness, the Menger and the Rothberger properties.
Lipparini, P. (2023). Products of topological spaces and families of filters. COMMENTATIONES MATHEMATICAE UNIVERSITATIS CAROLINAE, 64(3), 373-394 [10.14712/1213-7243.2024.005].
Products of topological spaces and families of filters
Paolo, Lipparini
2023-01-01
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 Lindelof if and only if all subproducts by <= omega(1) factors are Lindelof. Parallel results are obtained for final omega(n)-compactness, [lambda, mu]-compactness, the Menger and the Rothberger properties.File in questo prodotto:
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