Definition:Unit n-Cube

Theorem

Let $n \in \N$.

The unit $n$-cube $I^n$ is the Cartesian product of $n$ instances of the closed real interval $\set {x \in \R: 0 \le x \le 1}$:

$I^n = \closedint 0 1^n$

Sources

• 1975: Bert Mendelson: Introduction to Topology (3rd ed.) ... (previous) ... (next): Chapter $2$: Metric Spaces: $\S 7$: Subspaces and Equivalence of Metric Spaces: Example $2$