{"id":"palomar/PALOMAR-2026-08-19-000004","url":"https://github.com/vo-rodrigues/wallace-problem-palomar/tree/1ab2fb7ed1fb106e14af45312c2a7ab5d568048b","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-08-19-000004-v1.json","repo":"https://github.com/vo-rodrigues/wallace-problem-palomar","tags":["math.GR","math.GN","msc:22A05","msc:54H11","msc:54D20","msc:22A15","msc:20K20","msc:54A20","topological-groups","countable-compactness"],"score":0,"title":"vo-rodrigues/wallace-problem-palomar","trust":"high","domain":"math.GR","source":"palomar","authors":["Juliane Trianon Fraga","Vinicius de Oliveira Rodrigues"],"reviews":0,"subject":"math.GR","summary":"Lean 4 formalization of the theorem that every torsion-free Abelian group of cardinality continuum admits a Hausdorff countably compact group topology in which every convergent sequence is eventually constant, and constructs a commutative Tychonoff countably compact cancellative topological monoid that is not a group, giving a negative answer to Wallace's question.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-08-19","reactions":{},"formalized":true,"formalizes":[{"title":"The Wallace problem and countably compact torsion-free Abelian groups in ZFC","identifier":"arXiv:2608.17317v1","relationship":"formalizes"}]}