Let $f_1, \dots, f_N : \mathbb{R}^n \to \mathbb{R}^m$ each be an D3998: Odd euclidean real function.
Let $\sum_{n = 1}^N f_n$ be the D4344: Pointwise function sum of $f_1, \dots, f_N$.

Then $\sum_{n = 1}^N f_n$ is an D3998: Odd euclidean real function.