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Countable cellularity of arbitrary products via finite subproducts

Arthur Freitas Ramos, David Barros Hulak, Ruy Jose Guerra Barretto de Queiroz

Palomar Registrypalomar/PALOMAR-2026-10-19-000006Oct 19, 2026math.GNscore 0

An arbitrary product of topological spaces satisfies the countable chain condition (CCC) whenever every finite subproduct does. For nonempty factors this is an equivalence. The proof includes an indexed uncountable delta-system lemma that permits repeated finite supports, and glues compatible cylinders over a finite common root. Arbitrary products of separable spaces are consequently CCC, without a cardinal bound or separation assumptions and allowing empty factors. Continuous-surjection preservation and the discrete-space countability criterion are proved companions. No unrestricted…

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