We know by BCT that in a complete metric space the countable intersection of open dense sets is dense. Will it also be open?
2026-03-28 15:26:49.1774711609
Doubt related to Baire Category Theorem
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No.
Take the irrational numbers $\Bbb{I}$ on the real line.
We have that $\Bbb{I}=\bigcap_{n=1}^{\infty}O_n$ where $O_n$ are dense open sets.
But $\Bbb{I}$ is not open.