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Kuratowski–Ulam category theorem for countable pi-base spaces

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

Palomar Registrypalomar/PALOMAR-2026-10-20-000002Oct 20, 2026math.GNscore 0

For arbitrary topological spaces X and Y, if Y has a countable pi-base, a nowhere dense subset of X × Y has nowhere dense vertical sections outside a meagre subset of X. Meagre subsets likewise have meagre sections for residually many parameters, and residual subsets have residual sections. No Baire, separation or nonemptiness assumption is required for these forward results. For sets with the property of Baire, assuming both factors are Baire, meagreness and residuality are each equivalent to the corresponding generic section property. The product of two Baire spaces is consequently Baire…

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