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Concept
Local Invertibility
Local invertibility
refers to the property of a function where, at any given point within a certain neighborhood, the function behaves like an
invertible function
, enabling us to solve for
input values
from
output values
locally. This concept is crucial in calculus and
differential geometry
, particularly in the context of the
Inverse Function Theorem
, which ensures that a
differentiable function
is locally invertible near any point where its derivative (or Jacobian, in
higher dimensions
) is non-zero.
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