Baire paradoxical decompositions need at least 6 pieces

Friedrich Wehrung (1)

1 LMNO - Laboratoire de Mathématiques Nicolas Oresme

We prove that in certain cases, paradoxical decompositions of compact metric spaces using sets (or even $[0,1]$-valued functions) with the property of Baire modulo meager sets need more pieces than paradoxical decompositions with unrestricted pieces. In particular, any Baire paradoxical decomposition of the sphere $S^2$ using isometries needs at least six pieces.

Mots clés: Baire property; Paradoxical decomposition; Baire category

Domaines: Mathématiques générales [math.GM]; Topologie générale [math.GN]

Friedrich Wehrung. Baire paradoxical decompositions need at least 6 pieces. Proceedings of the American Mathematical Society, 1994, 121 (2), pp.643--644. ⟨10.1090/S0002-9939-1994-1209101-9⟩. ⟨hal-00004680⟩