{"id":"palomar/PALOMAR-2026-10-28-000020","url":"https://github.com/Arthur742Ramos/Math-Formalization/tree/2fb199d3c35ec0aa7c51bb4331de8c1f7ab31a07/topology/hewitt-savage-category","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-28-000020-v1.json","repo":"https://github.com/Arthur742Ramos/Math-Formalization","tags":["math.GN","math.DS","msc:54E52","msc:54B10","msc:37B02"],"score":0,"title":"Category Hewitt–Savage zero-one law for infinite Baire products","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":"A subset A of X^J with the property of Baire, invariant under every permutation moving only finitely many indices, is meagre or has meagre complement when J is infinite and the actual product space X^J is Baire. A corollary covers countable products of any Polish space. Finite-support displacement, cylinder mixing and the category contradiction are proved, not assumed.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-10-28","reactions":{},"formalized":true,"formalizes":[{"title":"A category analogue of the Hewitt–Savage zero-one law","identifier":"https://doi.org/10.1090/S0002-9939-1974-0345084-9","relationship":"formalizes"}]}