Open Research Index

Continuous open images of Polish spaces

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

Palomar Registrypalomar/PALOMAR-2026-10-22-000034Oct 22, 2026math.GNscore 0

Continuous open surjections preserve the strong Choquet property in arbitrary topological spaces. An explicit full-history strategy lifts each legal target play coherently, keeps the marked point, and maps an actual common source point. Consequently a continuous open metrizable image of a Polish space is Polish. A second-countable completely metrizable source gives a completely metrizable metrizable image. A regular Hausdorff codomain also suffices, by inherited second countability and Urysohn metrizability. These are classical results; no novelty or priority is claimed.

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