... 2(iii) Starting with the mapping θ (as given in the statement of Theorem2.9-2), we construct a mapping Θ that satisfies the assumptions of Theorem1.7-2. To this end, we define a mapping Θ :Ω→ ... continu-ously on the matrix field (gij) with respect to appropriate Fr´echet topologies.Sect. 1.1] Curvilinear coordinates 111.1 CURVILINEAR COORDINATES To begin with, we list some notations and conventions ... such an immersion exists, to what extent is it unique?As shown in Theorems 1.6-1 and 1.7-1, the answers turn out to be remarkablysimple to state (but not so simple to prove, especially the first...