Baire paradoxical decompositions need at least 6 pieces
Wehrung, Friedrich
HAL, hal-00004680 / Harvested from HAL
Text on HAL
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.
Publié le : 1994-07-05
Classification:  Baire category,  Paradoxical decomposition,  Baire property,  Primary 54E52, Secondary 54E45,  [MATH.MATH-GM]Mathematics [math]/General Mathematics [math.GM],  [MATH.MATH-GN]Mathematics [math]/General Topology [math.GN] 
@article{hal-00004680,
     author = {Wehrung, Friedrich},
     title = {Baire paradoxical decompositions need at least 6 pieces},
     journal = {HAL},
     volume = {1994},
     number = {0},
     year = {1994},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00004680}
}

Wehrung, Friedrich. Baire paradoxical decompositions need at least 6 pieces. HAL, Tome 1994 (1994) no. 0, . http://gdmltest.u-ga.fr/item/hal-00004680/