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Jul 23, 2020 at 10:12 comment added 0xbadf00d Thank you for your answer. Yes, I know this particular example. That's the point of (2.). The question is, why the desired conclusions are possible. The existence of $u$ as in this example shows that $H^{(r)}$ is not closed though.
Jul 23, 2020 at 9:41 history answered CrabMan CC BY-SA 4.0