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We survey results on partitioning some common sets into m congruent pieces, and prove that a ball in Rn cannot be so partitioned if 2 ≤ m ≤ n.
1.Cater, F. S., P 284,, Can. Math. Bull. 24 (1981) 382-383.Google Scholar
2
2.Dekker, T. J. and de Groot, J., Decompositions of a sphere, Proc. Int. Cong. Math. 2 (1954) 209.Google Scholar
3
3.Dekker, T. J. and de Groot, J., Decompositions of a sphere, Fund. Math. 43 (1956) 185-194.Google Scholar
4
4.Edelstein, M., On isometric complementary subsets of the unit hall, preprint.Google Scholar
5
5.Gustin, W., Partitioning an interval into finitely many congruent parts, Ann. Math. 54 (1951) 250-261.Google Scholar
6
6.Mazurkiewicz, S., Sur la décomposition d'un segment en une infinité d1ensembles non mesurables superposables deux à deux, Fund. Math. 2 (1921) 8-14.Google Scholar
7
7.Mycielski, J., On the paradox of the sphere, Fund. Math. 42 (1955) 348-355.Google Scholar
9.Mycielski, J., On the decomposition of a segment into congruent sets and related problems, Coll. Math. 5 (1957) 24-27.Google Scholar
10
10.Robinson, R. M., On the decomposition of spheres, Fund. Math. 34 (1947) 246-260.Google Scholar
11
11.Ruziewicz, S., Une application de l'equation functionelle f(x + y) = f(x) + f(y) à la décomposition de la droite en ensembles superposables non mesurables, Fund. Math. 5 (1924) 92-95.Google Scholar
12
12.Sierpiński, W., On the congruence of sets and their equivalence by finite decomposition, Lucknow, 1954, Reprinted, Bronx: Chelsea, 1967.Google Scholar
13
13.Von Neumann, J., Die Zerlegung Eines Intevalle In Abzählbar Viele Kongruente Teilmengen, Fund. Math. 11 (1928) 230-238.Google Scholar