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Jan 18, 2021 at 18:34 comment added Noah Schweber To clarify: the omission was intentional. That said, this is definitely relevant (and I didn't see the basis version argument before).
Jan 18, 2021 at 16:53 history edited Wojowu CC BY-SA 4.0
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Jan 18, 2021 at 16:51 comment added Wojowu @EmilJeřábek Ah, that's true. I was somewhat fooled by the motivational part. This makes the question significantly more difficult. I will think about it.
Jan 18, 2021 at 16:29 comment added Emil Jeřábek While your reading is perhaps more natural, the question does not actually stipulate $u\in f(u)$ (or $u\in\bigcap f(u)$ in the subbase version).
Jan 18, 2021 at 11:13 history edited Wojowu CC BY-SA 4.0
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Jan 18, 2021 at 10:14 history edited Wojowu CC BY-SA 4.0
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Jan 18, 2021 at 10:08 history answered Wojowu CC BY-SA 4.0