Timeline for Pointwise convergence for continuous functions
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| S Feb 3, 2016 at 10:46 | history | edited | András Bátkai |
I add a tag
|
|
| S Feb 3, 2016 at 10:46 | history | suggested | Ali Taghavi |
I add a tag
|
|
| Feb 3, 2016 at 10:40 | comment | added | Gro-Tsen | The keyword you want to search for is "Baire class 1" functions. See for example Kechris's Classical Descriptive Set Theory (Springer GTM 156), §24.B. One characterization is that $f\colon\mathbb{R}\to\mathbb{R}$ is pointwise limit of continuous functions iff $f^{-1}(U)$ is a countable union of closed sets for every open set $U$ (op. cit., 24.10). Its set of continuous points is then a comeager (hence dense) $G_\delta$ (op. cit., 24.14). | |
| Feb 3, 2016 at 10:14 | review | Suggested edits | |||
| S Feb 3, 2016 at 10:46 | |||||
| Feb 3, 2016 at 10:10 | answer | added | Ali Taghavi | timeline score: 6 | |
| Feb 3, 2016 at 9:21 | answer | added | smyrlis | timeline score: 6 | |
| Feb 3, 2016 at 9:14 | history | asked | Bazin | CC BY-SA 3.0 |