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Cantor dynamical extension with a dense forward orbit

Arthur Freitas Ramos, David Barros Hulak, Ruy Jose Guerra Barretto de Queiroz

Palomar Registrypalomar/PALOMAR-2026-10-28-000007Oct 28, 2026math.GNscore 0

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.

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