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Dec 6, 2022 at 8:30 comment added tom Thinking about it a bit more and you are most likely right. Smoothness depends only on bornology and I had a hope that maybe that would save me here as I accidentally assumed this statement at one point in my work.
Dec 5, 2022 at 18:23 comment added Christian Remling This doesn't sound like it can be true. Unless I misunderstood something, you're putting the compact-open topology on the second copy of $C^{\infty}$ and the much weaker topology of pointwise convergence on the first one.
Dec 5, 2022 at 17:07 history edited LSpice CC BY-SA 4.0
Mild typos
Dec 5, 2022 at 16:35 history asked tom CC BY-SA 4.0