👉 In mathematics, a diffeomorphism (or differentiable mapping) is a function that preserves both smoothness and orientation of curves in Euclidean space. This means that it maps paths in the Euclidean plane onto paths in the Euclidean plane, preserving orientation, but not necessarily changing the length or direction of the curve. For example, let's consider two functions f and g defined on the same open interval (a,b) of the real line: 1. f is differentiable at every
