Let $f : \mathbb{R}^n \to \mathbb{R}^m$ be a D992: Function.
Let $f_{\mathsf{odd}} : \mathbb{R}^n \to \mathbb{R}^m$ be the D4693: Function odd part of $f$.

Then $f_{\mathsf{odd}}$ is an D3998: Odd euclidean real function.