Timeline for Rudin PMA 4.31 - does the elements of $E$ have to be ordered (smallest to the biggest)?
Current License: CC BY-SA 4.0
5 events
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| Apr 12, 2023 at 19:09 | history | edited | GReyes | CC BY-SA 4.0 |
added 104 characters in body
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| Apr 12, 2023 at 19:01 | comment | added | GReyes | @krm2233 You are absolutely right of course. I will correct my answer. | |
| Apr 12, 2023 at 18:10 | comment | added | krm2233 | Indeed having managed to track down PMA, Rudin's point in giving this construction is to show that monotonic functions can be discontinuous at a dense set of points in their domain of definition: the function $f$ is continuous everywhere except on $E=\{x_n: n \in \mathbb N\}$. (Monotonic functions on an interval can have at most countably many discontinuities however.) | |
| Apr 12, 2023 at 17:11 | comment | added | krm2233 | The claim that $f$ is constant "close enough to $x_n$ for $x>x_n$ or $x<x_n$ is not correct. The set $\{x_n\}$ could be dense in $(a,b)$. | |
| Apr 12, 2023 at 16:37 | history | answered | GReyes | CC BY-SA 4.0 |