{"id":"palomar/PALOMAR-2026-10-28-000006","url":"https://github.com/Arthur742Ramos/Math-Formalization/tree/04f7b3ae1bf2e1ab42fb2b7c259176ed8ce143e8/topology/knaster-reichbach","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-28-000006-v1.json","repo":"https://github.com/Arthur742Ramos/Math-Formalization","tags":["math.GN","msc:54C20","msc:54F65","msc:54E45"],"score":0,"title":"Knaster–Reichbach homeomorphism extension on Cantor space","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":"Every homeomorphism between closed nowhere-dense subsets of Cantor space extends to a homeomorphism of the entire Cantor space, with exact pointwise agreement. Cantor space is the usual product topology on Nat -> Bool. Empty prescribed subsets are included. The proof constructs matched finite clopen refinements by alternating binary coordinate splits, then obtains mutually inverse continuous limit maps. Classical result; no novelty or priority claim.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-10-28","reactions":{},"formalized":true,"formalizes":[{"title":"Notion d’homogénéité et prolongements des homéomorphies","identifier":"https://eudml.org/doc/213323","relationship":"formalizes"},{"title":"On homogeneity of Cantor cubes","identifier":"https://arxiv.org/abs/2109.07214v2","relationship":"formalizes"},{"title":"Homeomorphisms on a Cantor set with subsequentially dense orbits","identifier":"https://www.tntech.edu/cas/pdf/math/techreports/TR-2012-4.pdf","relationship":"formalizes"}]}