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Sep 25, 2020 at 7:48 comment added Jaume You might want to find some extra hypothesis that align with some variation of Tietze's extension theorem (such as the set $\{x_m, m\in 1, 2,\dots\}$ being closed, only asking for a finite number of derivatives..).
Sep 25, 2020 at 7:41 history answered Jaume CC BY-SA 4.0