Timeline for Pointwise convergence for continuous functions
Current License: CC BY-SA 3.0
6 events
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| Feb 4, 2016 at 6:42 | history | edited | Ali Taghavi | CC BY-SA 3.0 |
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| Feb 3, 2016 at 16:56 | comment | added | Bazin | I am grateful for all the precise references. The Ali Taghavi explicit example is illuminating. | |
| Feb 3, 2016 at 10:40 | comment | added | Ali Taghavi | @Gro-Tsen +1 thank you. Very interesting comment. | |
| Feb 3, 2016 at 10:34 | comment | added | Gro-Tsen | Amusingly, the function $\mathbf{1}_{\mathbb{Q}}$ taking the value $1$ on the rationals and $0$ on the irrationals, which is discontinuous everywhere, is not (as per smyrlis's answer) pointwise limit of continuous functions (=Baire class 1), but it is (Baire class 2) pointwise limit of functions like this one which are themselves pointwise limits of continuous functions. So pointwise limits of pointwise limits are not necessarily pointwise limits. | |
| Feb 3, 2016 at 10:22 | history | edited | Ali Taghavi | CC BY-SA 3.0 |
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| Feb 3, 2016 at 10:10 | history | answered | Ali Taghavi | CC BY-SA 3.0 |