{"id":"palomar/PALOMAR-2026-10-22-000034","url":"https://github.com/Arthur742Ramos/Math-Formalization/tree/dfbeea7108d04be545185d5f868efbcd9c86c6e5/topology/open-polish-images","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-22-000034-v1.json","repo":"https://github.com/Arthur742Ramos/Math-Formalization","tags":["math.GN","msc:54C10","msc:54E50","msc:54E52","msc:91A44","general-topology","polish-spaces","open-maps","descriptive-set-theory"],"score":0,"title":"Continuous open images 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":"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.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-10-22","reactions":{},"formalized":true,"formalizes":[{"title":"Stationary and convergent strategies in Choquet games, arXiv:0907.4126v2","identifier":"https://arxiv.org/pdf/0907.4126v2","relationship":"formalizes"},{"title":"Notes on quasi-Polish spaces","identifier":"https://rynchn.github.io/math/qpol.pdf","relationship":"formalizes"}]}