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Knaster–Reichbach homeomorphism extension on Cantor space

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

Palomar Registrypalomar/PALOMAR-2026-10-28-000006Oct 28, 2026math.GNscore 0

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.

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