In differential geometry, a part of mathematics, a local diffeomorphism is intuitively seen as a function between smooth varieties, which maintains the local differentiable structure.
The formal definition of a local diffeomorphism is given below. Formal definition
Let X and Y be differentiable varieties. A function, f : X & # x2192; Y {\displaystyle f:X\to Y\,}
is a local diffeomorphism, if x exists for each point, x in an open set, U, containing x such that f ( U ) {\displaystyle f(U)\,}
is open in y and f | U : U & # x2192; f ( U ) {\displaystyle f|_{U}:U\to f(U)\,}
is a diffeomorphism.
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