Definition:Decomposable Set

Definition
A set $$S \subset \R^n \ $$ is decomposable in $$m \ $$ sets $$A_1,\dots, A_m \subset \R^n \ $$ if there exist isometries $$\phi_1,\ldots,\phi_m: \R^n \to \R^n \ $$ such that:


 * 1) $$S = \bigcup_{k=1}^m \phi_k(A_k) \ $$
 * 2) For $$i \neq j, \phi_i(A_i) \cap \phi_j(A_j) = \varnothing \ $$