Timeline for Continuous function on colimit
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 14, 2020 at 10:07 | vote | accept | ABIM | ||
| Feb 14, 2020 at 8:22 | comment | added | Jochen Wengenroth | I don't understand what you mean by $X$ is considered with the colimit topology: Only $Y=\bigcup_n X_n$ has a colimit topology and (as Yemon mentions) $Y$ is hardly ever equal to $X$. And I don't see how density of $Y$ in $(X,\|\cdot\|)$ should help -- this does not mean that $X$ is a completion of $Y$ (which need not be complete but easily can be, e.g., is all $X_n$ are closed subspaces of $X$ or if all $X_n$ are reflexive). | |
| Feb 13, 2020 at 23:26 | answer | added | Sasha | timeline score: 2 | |
| Feb 13, 2020 at 22:00 | comment | added | ABIM | Yes, I oversimplified things. Dense and also in the category LCS (with continuous linear maps as morphisms). | |
| Feb 13, 2020 at 21:59 | history | edited | ABIM | CC BY-SA 4.0 |
added 10 characters in body
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| Feb 13, 2020 at 21:59 | comment | added | Yemon Choi | Also, colimit in what category? | |
| Feb 13, 2020 at 21:58 | comment | added | Yemon Choi | Do you mean that $\bigcup_n X_n$ is dense in $X$ or equal to $X$? I think the latter scenario is ruled out (assuming the $X_n$ are strictly increasing) by a Baire category argument | |
| Feb 13, 2020 at 21:23 | history | edited | YCor | CC BY-SA 4.0 |
removed capitals, added tag
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| Feb 13, 2020 at 21:14 | history | asked | ABIM | CC BY-SA 4.0 |