Timeline for A problem in real analysis of a topological nature
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 26, 2018 at 17:09 | vote | accept | James Baxter | ||
| Dec 26, 2018 at 17:01 | answer | added | Nate Eldredge | timeline score: 7 | |
| Dec 26, 2018 at 16:44 | comment | added | Nate Eldredge | @MartinKell: It's true that $f|_S$ will extend to a uniformly continuous function (call it $g$), but $f$ need not agree with $g$ on $S^c$, so we cannot conclude that $f$ is uniformly continuous. | |
| Dec 26, 2018 at 16:27 | comment | added | Martin Kell | If $f|_S$ is uniformly continuous then it can be natuarlly extended to a uniformly continuous function on the closure of $S$. Hence $f$ itself has to be uniformly continuous. If you weaken the assumption to "there is a sequence of sets $S_n$ such that their union is dense in $R$ and f restricted to $S_n$ is uniformly continuous on $S_n$" then it's true for measurable functions by Lusin's Theorem. | |
| Dec 26, 2018 at 14:58 | history | asked | James Baxter | CC BY-SA 4.0 |