\begin{definition}[Definition:Hilbert Cube/Definition 2]
The '''Hilbert cube''', denoted by $I^\omega$, is defined as:
:$\ds I^\omega := \set {\sequence {x_n}_{n \mathop \in \N} \in \R^\N: 0 \le x_n \le \frac 1 n}$
\end{definition}