{"id":"palomar/PALOMAR-2026-10-28-000007","url":"https://github.com/Arthur742Ramos/Math-Formalization/tree/94b2a53e704d125161101ab9d0deefe54cfe4aea/topology/cantor-dynamical-extension","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-28-000007-v1.json","repo":"https://github.com/Arthur742Ramos/Math-Formalization","tags":["math.GN","math.DS","msc:54C20","msc:37B02","msc:37B10"],"score":0,"title":"Cantor dynamical extension with a dense forward orbit","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 of a closed nowhere-dense subset A of the usual Cantor space Nat -> Bool extends pointwise to an ambient homeomorphism H with a dense forward orbit. Empty A is included. The proof constructs an orbit embedding into the two-sided full shift, extends it using Knaster–Reichbach, proves forward shift orbit density by finite-coordinate patching and Baire, and conjugates back. Classical invariant-subset case only; no novelty claim.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-10-28","reactions":{},"formalized":true,"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"}]}