Displaying similar documents to “Rosenthal compacta and NIP formulas”

On countable families of sets without the Baire property

Mats Aigner, Vitalij A. Chatyrko, Venuste Nyagahakwa (2013)

Colloquium Mathematicae

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We suggest a method of constructing decompositions of a topological space X having an open subset homeomorphic to the space (ℝⁿ,τ), where n is an integer ≥ 1 and τ is any admissible extension of the Euclidean topology of ℝⁿ (in particular, X can be a finite-dimensional separable metrizable manifold), into a countable family ℱ of sets (dense in X and zero-dimensional in the case of manifolds) such that the union of each non-empty proper subfamily of ℱ does not have the Baire property...

Invariant Borel liftings for category algebras of Baire groups

Maxim R. Burke (2007)

Fundamenta Mathematicae

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R. A. Johnson showed that there is no translation-invariant Borel lifting for the measure algebra of ℝ/ℤ equipped with Haar measure, a result which was generalized by M. Talagrand to non-discrete locally compact abelian groups and by J. Kupka and K. Prikry to arbitrary non-discrete locally compact groups. In this paper we study analogs of these results for category algebras (the Borel σ-algebra modulo the ideal of first category sets) of topological groups. Our main results are for the...