Timeline for When is a locally convex topological vector space normal or paracompact?
Current License: CC BY-SA 4.0
6 events
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| Apr 1, 2020 at 0:56 | history | edited | Robert Furber | CC BY-SA 4.0 |
Changed reference to Waelbroeck from springerlink to link.springer.com, as it was a dead link, made it more specific to the precise statement as well.
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| Dec 16, 2009 at 8:59 | comment | added | Andrew Stacey | It's been a while since I first worked on this problem and I'd forgotten some of the subtleties. In particular, reading your answer again I recall that I'm interested in both the inductive LCTVS topology and the inductive topology (over inclusions of finite dimensional subspaces) so your answer on the latter is still very useful even though it's not directly an answer of the stated question! | |
| Dec 14, 2009 at 21:19 | history | edited | Greg Kuperberg | CC BY-SA 2.5 |
Major correction
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| Dec 14, 2009 at 19:34 | comment | added | Greg Kuperberg | Well, geez. I need to review whether or not it is finer than the box topology. If so, that is a mistake already, but not the essential point. What I really may need, whether or not it is the box topology, is that this l.c. inductive limit happens to equal the topological inductive limit. I construct a Tietze function by transfinite induction. I should also simplify and reword the argument a bit, but first let me review whether or not it works. | |
| Dec 14, 2009 at 18:56 | comment | added | Andrew Stacey | This is going to take me a while to parse. First question: you say that the direct limit for direct sums in LCTVS is the box topology. Do you have a reference for that? Is it peculiar to having a limit ordinal? I seem to be able to construct a neighbourhood using an infinite simplex that doesn't contain a box, but I may well be wrong. | |
| Dec 12, 2009 at 8:15 | history | answered | Greg Kuperberg | CC BY-SA 2.5 |