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Mycielski Cantor independent set for dense-open binary relations

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

Palomar Registrypalomar/PALOMAR-2026-10-28-000011Oct 28, 2026math.GNscore 0

Every nonempty open subset U of a perfect Polish space X contains a closed topological embedding e of Cantor space Nat -> Bool such that every ordered pair of distinct image points lies in each member of a countable family of dense-open subsets R_n of X × X. Coordinated finite refinements enforce all ordered pairs, have closure nesting and vanishing diameter; ambient completeness yields the Cantor limit map. Single-Cantor binary-relation scope only; no novelty claim.

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