Cantor Space is Meager in Closed Unit Interval

Theorem
Let $T = \struct {\CC, \tau_d}$ be the Cantor space.

Then $T$ is meager in $\closedint 0 1$.

Proof
From Cantor Space is Nowhere Dense, $T$ is nowhere dense in $\closedint 0 1$.

So, trivially, $\CC$ is the union of nowhere dense subsets of $\closedint 0 1$.

Hence the result from definition of meager.