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Countable-coordinate factorization for compact products

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

Palomar Registrypalomar/PALOMAR-2026-10-17-000015Oct 17, 2026math.GNscore 0

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…

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