Timeline for Continuity in Banach space for non-linear maps
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
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| Nov 21, 2014 at 17:56 | history | edited | Nik Weaver | CC BY-SA 3.0 |
added 12 characters in body
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| Nov 21, 2014 at 17:52 | comment | added | Nik Weaver | Yeah, good point. Corrected. | |
| Nov 21, 2014 at 16:31 | comment | added | Pietro Majer | I think it is safer to have the family of balls locally finite too, and not only disjoint. Or also, to have the support of $f_n$ into the ball of radius $\epsilon/2$. Otherwise the resulting glueing function may fail to be continuous. For instance, in $\ell_\infty$ the unit balls centered at $(1+1/n)e_n$ are disjoint and well separated from each other, but any nbd of $0$ meets almost all of them, which allows the glued $f$ to be possibly discontinuous. | |
| Nov 21, 2014 at 15:57 | history | answered | Nik Weaver | CC BY-SA 3.0 |