We consider conditions under which an upper semicontinuous decomposition has the decomposition space which is a topological nsphere. A special emphasis is placed on the case in which the decomposition has only a countable number of nondegenerate elements. If M is an n-manifold with boundary, Bd M and Int M will be used to denote the usual boundary and the interior of M. The set theoretical boundary of a subset A in a space will be denoted by b(A) and the closure of A by Cl A.