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Products of sequentially compact spaces with no separability assumption
Lipparini, Paolo
2022
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e-ISSN
2464-8728
Abstract
Let X be a product of topological spaces. We prove that X is sequentially compact if and only if all subproducts by ≤ s factors are sequentially compact. If s = h, then X is sequentially compact if and only if all factors are sequentially compact and all but at most < s factors are ultraconnected. We give a topological proof of the inequality cf s ≥ h. Recall that s denotes the splitting number and h the distributivity number. Some corresponding invariants are introduced, relative to an arbitrary topological property, more generally, relative to a subset of a partial infinitary semigroup.
Publisher
EUT Edizioni Università di Trieste
Source
Paolo Lipparini, "Products of sequentially compact spaces with no separability assumption" in: "Rendiconti dell’Istituto di Matematica dell’Università di Trieste: an International Journal of Mathematics vol.54 (2022)", EUT Edizioni Università di Trieste, Trieste, 2022, pp. 69-77
Languages
en
Rights
Attribution-NonCommercial-NoDerivatives 4.0 Internazionale
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