Open Research Index

Category Hewitt–Savage zero-one law for infinite Baire products

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

Palomar Registrypalomar/PALOMAR-2026-10-28-000020Oct 28, 2026math.GNscore 0

A subset A of X^J with the property of Baire, invariant under every permutation moving only finitely many indices, is meagre or has meagre complement when J is infinite and the actual product space X^J is Baire. A corollary covers countable products of any Polish space. Finite-support displacement, cylinder mixing and the category contradiction are proved, not assumed.

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