Interpreting vector space 'raised' to a time space

Question

Time series data is sometimes written as $w \in \mathbb{W}^\mathbb{T}$ where $\mathbb{W}$ is a vector space and $\mathbb{T}\subseteq\mathbb{R}$ is some time space (usually $\mathbb{R}$ or $\mathbb{Z}$). What is the proper interpretation of the space $\mathbb{W}^\mathbb{T}$?

Answer 1

The object $w \in \Bbb W^{\Bbb T}$ is a family $\{w_t\}$ of vectors $w_t \in \Bbb V$ indexed by $t \in \Bbb T$, or equivalently, a function $\Bbb T \to \Bbb W$.

More generally, for any sets $X, Y$, the notation $Y^X$ is often used for the set of functions $X \to Y$.