Timeline for Example: a locally convex TVS which is not compactly generated
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
|
|
| Apr 29, 2014 at 7:24 | comment | added | janacek | This question has been answered but the following remark might be of interest since it gives a unified method which allows one to answer many related ones. Suppose that one has a topological property which is stable under the formation of closed subsets as is that of being a $k$-space (the standard name for the property in question). Then if you can find a completely regular space which fails the property, you can find a lcs which fails. This follows immediately from the fact every such space embeds in a canonical manner as a closed subspace of its so-called free lcs. | |
| Apr 28, 2014 at 22:01 | vote | accept | Tom LaGatta | ||
| Apr 28, 2014 at 21:57 | answer | added | Francois Ziegler | timeline score: 9 | |
| Apr 28, 2014 at 21:54 | comment | added | Johannes Hahn | I do not have a proof nor a counterexample. But I'd like to note that bornological LCTVS are compactly generated so that the classical examples for LCTVS test functions and distributions will not give us counterexamples. Furthermore the full subcategory of compactly generated LCTVS is closed under colimit and more generally under taking "final objects" (in the sense of "final topology" form point set topology, not in the sense of "terminal object" from category theory. Is there a standard name for analogues of initial and final topologies?) | |
| Apr 28, 2014 at 21:15 | history | edited | Tom LaGatta | CC BY-SA 3.0 |
added 104 characters in body
|
| Apr 28, 2014 at 20:53 | history | asked | Tom LaGatta | CC BY-SA 3.0 |