Concentric Tori in the Three-Spere

A torus is the topological product of two circles, while a solid torus is the topological product of a circle and a disk. Two solid tori B1 and B2 in the three-sphere S^3, with B2 interior to B1, are said to be concentric if and only if the closure of B1-B2 (the set of points in B1 but not in B2) is homeomorphic to the topological product of a torus and a closed interval. Two tori in S^3 are concentric if and only if they are respectively the boundaries of two concentric solid tori.