Closed Unit Interval is Homeomorphic to Letter L

Theorem
Let $\R$ be the real number line under the Euclidean metric.

Let $\Bbb I := \closedint 0 1$ be the closed unit interval.

Let $\mathsf L \subseteq \R^2$ denote the letter $L$:
 * $\mathsf L := \closedint 0 1 \times \set 0 \cup \set 0 \times \closedint 0 1$

Then $\Bbb I$ and $\mathsf L$ are homeomorphic.