Meaning of the function notation $\mathbf{y}=(y(t_1), y(t_2), \dots, y(t_m))$?

Question

I don't grasp the following function notation: $$ \mathbf{y}=(y(t_1), y(t_2), \dots, y(t_m)) \tag 1 $$ For $\mathbf{g}=(g_1(t), g_2(t),\dots, g_m(t))$ we have $\mathbf g:\mathbb R\rightarrow \mathbb R^m$, but how can I specify the domain and range for $(1)$, i.e. $$ \mathbf y:\mathbb R^?\rightarrow \mathbb R^? \quad ? $$

Answer 1

There are $m$ independant variables, so the domain is $\mathbb R^m$ (assuming all those variables are in $\mathbb R$). The output is a vector in $\mathbb R^m$. So:$$\mathbf y: \mathbb R^m\to \mathbb R^m.$$