I'm having difficulty with the following question:
Show that, for $\mathbb{F} \in \{\mathbb{R}, \mathbb{C}\}$ and for an infinite discrete time-domain $\mathbb{T}$, $\exists$ an isomorphism of normed vector spaces between $(c_{fin}(\mathbb{T},\mathbb{F}),||\cdot||_{\infty})$ and $(c_{fin}(\mathbb{Z}_{>0},\mathbb{F}),||\cdot||_{\infty})$
I know I can find a bijection, $g$, between the countably-infinite $\mathbb{T}$ and $\mathbb{Z}_{>0}$. If I can find $f \in \mathbb{F}^{\mathbb{Z}_{>0}}$, then $f\circ g$ is a map from $\mathbb{F}^{\mathbb{Z}_{>0}} \rightarrow \mathbb{F}^{\mathbb{T}}$. I don't know how if, I restrict $f$ to $c_{fin}(\mathbb{Z}_{>0},\mathbb{F}),||\cdot||_{\infty})$, I can show $f\circ g$ is an isomorphism.