Cantor Space is Meager in Closed Unit Interval

Theorem
Let $T = \left({\mathcal C, \tau_d}\right)$ be the Cantor space.

Then $T$ is meager in $\left[{0 \,.\,.\, 1}\right]$.

Proof
From Cantor Space is Nowhere Dense, $T$ is nowhere dense in $\left[{0 \,.\,.\, 1}\right]$.

So, trivially, $\mathcal C$ is the union of nowhere dense subsets of $\left[{0 \,.\,.\, 1}\right]$.

Hence the result from definition of meager.