Open Research Index

The strong Choquet characterization of Polish spaces

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

Palomar Registrypalomar/PALOMAR-2026-10-22-000001Oct 22, 2026math.GNscore 0

For every second-countable metrizable topological space, the second player has a winning full-history strong Choquet strategy if and only if the topology admits a complete metric, equivalently if and only if the space is Polish. Moves include a marked point which every response must retain. The difficult converse constructs a coherent countable response tree, proves the embedded image is Gδ, and transfers complete metrizability from the metric completion. Supporting results prove complete-metric winning strategies without second countability, complete metrizability of Gδ subsets of arbitrary…

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