Timeline for Algebraic and continuous duals of an inverse limit of finite dimensional vector spaces
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Jul 10 at 22:49 | history | edited | LSpice | CC BY-SA 4.0 |
Transcribed image; change `*` for footnote to ¹ to avoid tripping MathJax parser; deleted "thanks, Tom"
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| Jul 10 at 16:58 | history | became hot network question | |||
| Jul 10 at 14:09 | vote | accept | Tom Adams | ||
| Jul 10 at 13:49 | answer | added | Jochen Wengenroth | timeline score: 6 | |
| Jul 10 at 12:54 | comment | added | Tom Adams | Thank you! I hadn't used anywhere that the inductive limit topology is the final topology. I can see how these facts prove that $(Y')' = (Y')^*$ because there we are interested in maps from an inductive limit into $K$. However, I can't see how they establish that $Y' = Y^*$ because there we are looking at maps from a projective limit (which is equipped with an initial topology) and so its harder to use the first fact you mentioned about finite dimensional vector spaces. I'm probably missing something obvious. It wouldn't be the first time! I'll think through what you have written again :) | |
| Jul 10 at 12:50 | history | edited | Tom Adams | CC BY-SA 4.0 |
added 3 characters in body
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| Jul 10 at 12:12 | comment | added | terceira | This is a combination of two facts which workfor the real and complex fields, presumably also in the general situation: a linear mapping on a finite dimensional tvs is automatically continuous and such a mapping on an inductive limit space is continuous if and only it is so on each component. | |
| Jul 10 at 8:58 | history | asked | Tom Adams | CC BY-SA 4.0 |