{"id":"palomar/PALOMAR-2026-10-17-000015","url":"https://github.com/Arthur742Ramos/Math-Formalization/tree/fc3f403c4d07356d2232e809f326f63a9ce9da45/topology/countable-coordinate-factorization","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-17-000015-v1.json","repo":"https://github.com/Arthur742Ramos/Math-Formalization","tags":["math.GN","msc:54B10","msc:54C05","msc:54E35","general-topology","compact-spaces","metrizability"],"score":0,"title":"Countable-coordinate factorization for compact products","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":"Every continuous map from an arbitrary product of nonempty compact Hausdorff spaces into a metrizable space factors continuously through a countable subproduct. A uniform-space proof establishes countable coordinate dependence for uniformly continuous maps into separated countably generated uniform spaces. The factor for a fixed coordinate set is unique. Countably many maps share a countable coordinate set. Continuous injections into metrizable targets force only countably many nontrivial factors, giving the exact metrizability criterion for nonempty compact Hausdorff products. Empty index…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-10-17","reactions":{},"formalized":true,"formalizes":[{"title":"On α-embedded subsets of products, arXiv:1411.3173v1","identifier":"https://arxiv.org/pdf/1411.3173v1","relationship":"formalizes"}]}