Proofs for the Open Mapping Theorem that I've seen use the Baire Category Theorem to produce an open set in $Y$ that is in the image of some scaled ball from $X$. I think I'm missing a technical point though -- why can't we take for granted that an open subset is available in the image?
2026-03-25 22:10:37.1774476637
Why is Baire Category Important in the Open Mapping Theorem
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