{"id":"palomar/PALOMAR-2026-10-22-000001","url":"https://github.com/Arthur742Ramos/Math-Formalization/tree/f2ee17b609eec4788b85043f8ad504a63cd69d86/topology/strong-choquet-polish","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-22-000001-v1.json","repo":"https://github.com/Arthur742Ramos/Math-Formalization","tags":["math.GN","msc:54E50","msc:54E52","msc:91A44","general-topology","game-theory","polish-spaces","descriptive-set-theory"],"score":0,"title":"The strong Choquet characterization of Polish spaces","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":"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…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-10-22","reactions":{},"formalized":true,"formalizes":[{"title":"On complete metrizability of the Hausdorff metric topology, arXiv:1503.04383v1","identifier":"https://arxiv.org/pdf/1503.04383v1","relationship":"formalizes"},{"title":"Preservation and Destruction in Simple Refinements","identifier":"https://wrbrian.wordpress.com/wp-content/uploads/2012/01/refinements1.pdf","relationship":"formalizes"},{"title":"Stationary and convergent strategies in Choquet games, arXiv:0907.4126v2","identifier":"https://arxiv.org/pdf/0907.4126v2","relationship":"formalizes"}]}