Multivalued function: Difference between revisions

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==Inverses of functions==
 
If ''f : X → Y'' is an ordinary function, then its inverse is the multivalued function
:<math> \Gamma_{f^{-1}}\ \subseteq \ Y\times X</math>
defined as ''Γ<sub>f</sub>'', viewed as a subset of ''X'' × ''Y''. When ''f'' is a [[differentiable function]] between [[Manifold|manifolds]], the [[Inverse function theorem|inverse function theorem]] gives conditions for this to be single-valued locally in ''X''.