Timeline for Closedness of finite-dimensional subspaces
Current License: CC BY-SA 2.5
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 5, 2016 at 5:37 | comment | added | LSpice | I just needed to cite this result in a paper, and literally thought "I know that this result must be somewhere in Bourbaki, but don't want to go hunting; let me Google MO instead, and hope that someone has already done the hunting for me." Thank you for being that one! | |
| Jul 24, 2011 at 6:28 | comment | added | Harry Altman | Quick note: This argument seems to also work for ordered fields as well as valued fields. No idea about other fields. | |
| Sep 9, 2010 at 17:26 | vote | accept | CommunityBot | ||
| Sep 8, 2010 at 11:11 | comment | added | Pierre-Yves Gaillard | Thanks! I can't really say I KNOW the notion of uniform space. I just knew such a notion existed, I thought (apparently correctly) that it was due to Weil, and I knew it played an important role in several Bourbaki's books... It's one of the many things I'm planning to learn sometime... | |
| Sep 8, 2010 at 10:52 | comment | added | user5810 | Yeah, I haven't been able to come up with one either. I just thought it was possible you didn't know how a complete field would be defined without an absolute value. | |
| Sep 8, 2010 at 10:18 | comment | added | Pierre-Yves Gaillard | Thank you! Do you mean Example 3 in en.wikipedia.org/wiki/Uniform_space#Examples ? I don't see there an example of complete topological field whose topology is not given by an absolute value. | |
| Sep 8, 2010 at 9:46 | comment | added | user5810 | Your answer is still more general (and so better) than Robin's. [If you don't know what another kind of complete field would be, see Definition, Completeness, and Example 3 at en.wikipedia.org/wiki/Uniform_space ] | |
| Sep 8, 2010 at 9:01 | comment | added | Pierre-Yves Gaillard | I'm afraid I misunderstood your question. I took it for granted that you considered only fields complete with respect to a nontrivial absolute value. Sorry. [I know nothing about other kinds of complete fields.] | |
| Sep 8, 2010 at 8:30 | comment | added | user5810 | How do you show that every complete field has an absolute value that induces its topology? | |
| Sep 8, 2010 at 7:32 | comment | added | Pierre-Yves Gaillard | You asked if a finite dimensional space F in a Hausdorff topological vector space over a complete field is always closed. The result I prove (following Bourbaki) shows that F (equipped with the induced topology) is complete, and thus closed. | |
| Sep 8, 2010 at 7:11 | comment | added | user5810 | Umm, I wouldn't have known how to prove this result, but I don't see how it addresses my question, either. | |
| Sep 8, 2010 at 4:21 | history | answered | Pierre-Yves Gaillard | CC BY-SA 2.5 |