Timeline for Can $L^1_{loc}$ be represented as colimit?
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
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| May 3, 2020 at 12:22 | comment | added | ABIM | Great! Thanks I'll have a look at this paper. Thanks Jochen | |
| May 3, 2020 at 11:30 | comment | added | Jochen Wengenroth | I did not know that paper. Such weighted spaces of integrable functions had been investigated long time ago e.g. by Konrad Reiher ''Weighted inductive and projective limits of normed Köthe function spaces'', Results in Math.13, 147–161(1988). | |
| May 3, 2020 at 10:25 | comment | added | ABIM | Your weighted $L^1$ comment refers to this paper, no?: kurims.kyoto-u.ac.jp/EMIS/journals/RCM/Articulos/763.pdf | |
| Jan 14, 2020 at 9:23 | history | edited | ABIM | CC BY-SA 4.0 |
added 113 characters in body
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| Dec 9, 2019 at 14:26 | history | bounty ended | ABIM | ||
| Dec 3, 2019 at 14:37 | comment | added | Jochen Wengenroth | By definition, the colimit topology in TOP is the finest topology making the inclusions continuous hence it is finer than the colimit topology in LCS. I believe that the TOP-colimit is even strictly finer but I don't have an argument for this. | |
| Dec 3, 2019 at 12:08 | comment | added | ABIM | But how can one show that in TOP this colimit is finer, explicitly? | |
| Dec 3, 2019 at 11:05 | comment | added | Jochen Wengenroth | Yes, the countable inductive limit of separable spaces is separable (the union of countable dense subsets of the steps is dense in the inductive limit). | |
| Dec 3, 2019 at 7:18 | comment | added | Jochen Wengenroth | "Older" books on Functional Analysis usually treated inductive limits. E.g., Köthe's Topological Vector Spaces I, Jarchow's Locally Convex Spaces or Bonet & Perez-Carreras' Barrelled Locally Convex Spaces. | |
| Dec 1, 2019 at 17:21 | comment | added | ABIM | This answer is fantastic, however it uses some concepts I'm not fully familier with. Would it be possible to add some references (which you feel are good). I can give a small bounty for that in a couple days. Also, is there a classical interpretation/application of the colimit in LCS? | |
| Dec 1, 2019 at 17:20 | vote | accept | ABIM | ||
| Dec 1, 2019 at 14:13 | history | answered | Jochen Wengenroth | CC BY-SA 4.0 |