What is the regular value of a manifold?

Crucially, a regular value is distinguished by the fact that it is not a critical value. A critical value arises when the map f fails to be locally invertible at a specific point, known as a critical point.

In the realm of differential geometry, the concept of a regular value holds significant importance.

It pertains to a map f, which is a function between smooth manifolds. A smooth manifold is a type of topological space that locally resembles Euclidean space, allowing for the study of smooth curves and surfaces on it.

A regular value of the map f is defined as an element within the codomain of f. The codomain is the set that contains all possible output values of the function.

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