Nash’s implicit function theorem is generalized. The analytical results are applied to the problem of isometric immersion; in particular, the realizability in Euclidean space of real-analytic Riemannian manifolds is demonstrated. Moreover, theorems about the existence, approximation, extension and transversality of isometric immersion and related maps are stated; deformations and questions about unique definability are also investigated. In addition to the implicit function theorem, the theory of topological sheaves is used.
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