# Cantor Space is Non-Meager in Itself

## Theorem

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

Then $T$ is non-meager in itself.

## Proof

We have that the Cantor Space is Complete Metric Space.

By Baire Category Theorem, a complete metric space is also a Baire space.

The result then follows by Baire Space is Non-Meager.

$\blacksquare$