Cantor Space is Non-Meager in Itself
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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.
$\blacksquare$
Sources
- 1978: Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (2nd ed.) ... (previous) ... (next): Part $\text {II}$: Counterexamples: $29$. The Cantor Set: $4$