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Real-valued functions of real variable, analytic properties of functions and sequences, limits, continuity, smoothness of these.

6 votes
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135 views

Injectiveness of a monotonic surjective mapping $\mathbb R^n \to \mathbb R^n$ with $\det J \...

Consider a surjective mapping $F \colon \mathbb R^n \to \mathbb R^n$, $F\in C^1$, $\dfrac{\partial F_i}{\partial x_j} > 0$, and $\det \left(\!\left( \dfrac{\partial F_i}{\partial x_j} \right)\!\right …
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