{"id":"palomar/PALOMAR-2026-10-19-000006","url":"https://github.com/Arthur742Ramos/Math-Formalization/tree/92f1a925329465c86a96b2f612fcd0d5345eed3b/topology/product-countable-chain-condition","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-19-000006-v1.json","repo":"https://github.com/Arthur742Ramos/Math-Formalization","tags":["math.GN","msc:54B10","msc:54A25","general-topology","chain-condition","products"],"score":0,"title":"Countable cellularity of arbitrary products via finite subproducts","trust":"high","domain":"math.GN","source":"palomar","authors":["Arthur Freitas Ramos","David Barros Hulak","Ruy Jose Guerra Barretto de Queiroz"],"reviews":0,"subject":"math.GN","summary":"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…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-10-19","reactions":{},"formalized":true,"formalizes":[{"title":"Is the product of ccc spaces a ccc space?, Publicacions Matematiques 33 (1989), 173–183","identifier":"https://ddd.uab.cat/pub/pubmat/pubmat_a1989v33n2/pubmat_a1989v33n2p173.pdf","relationship":"formalizes"}]}