# Cantor Space is Non-Meager in Itself

From ProofWiki

## Theorem

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

Then $T$ is non-meager in itself.

## Proof

We have that the Cantor Space is Complete Metric Space.

## Sources

- 1970: Lynn Arthur Steen and J. Arthur Seebach, Jr.:
*Counterexamples in Topology*... (previous) ... (next): $\text{II}: \ 29: \ 4$