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Let $V\subset \mathbb{R}^n$ be a connected, open set and $f:V\rightarrow \mathbb{R}^m$ be a map. Suppose that for all $x$,$y\in V$ ,

$|f(x)-f(y)|_*\leqslant|x-y|_\diamond ^\frac{3}2{}$,

where $| \ |_*$ (respectively $| \ |_\diamond$) is a norm on $\mathbb{R}^n$ (respectively $\mathbb{R}^m$). Prove that $f$ is constant.

(How could $f$ be constant? How to prove this? Thank you.)

$|f(x)-f(y)|_*\leqslant|x-y|_\diamond ^\frac{3}2{}$,

where $| \ |_*$ (respectively $| \ |_\diamond$) is a norm on $\mathbb{R}^n$ (respectively $\mathbb{R}^m$). Prove that $f$ is constant.

(How could $f$ be constant? How to prove this? Thank you.)

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