Timeline for Non-equivalent norms on finite dimensional vector spaces over a non-complete field
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Nov 15, 2022 at 17:23 | comment | added | Gerald Edgar | @FawzyHegab All norms on the two-dimensional vector space are equivalent, provided the field is complete (as the OP noted). So counterexamples must use an incomplete field. Non-archimedean? Try to do it where the field is $\mathbb Q$ with the $p$-adic absolute value (do not complete it to the $p$-adic numbers). Imitate the proof above, but in place of $\sqrt{2}$ use an irrational $p$-adic number. | |
| Nov 15, 2022 at 0:46 | comment | added | FNH | Do you know any example in the case of Non-archimedean norms? @GeraldEdgar | |
| Mar 22, 2017 at 6:46 | vote | accept | Garoal | ||
| Mar 21, 2017 at 18:06 | comment | added | Tom Goodwillie | Yes, I'm probably wrong. | |
| Mar 21, 2017 at 17:47 | comment | added | Gerald Edgar | @TomGoodwillie ... The OP should tell us if Tom is right. If so, please provide a definition of "norm" for us. (The usual definition says real values, even for a non-real field.) | |
| Mar 21, 2017 at 17:42 | comment | added | Tom Goodwillie | But I think the norm was meant to take values in the given field. | |
| Mar 21, 2017 at 17:31 | history | answered | Gerald Edgar | CC BY-SA 3.0 |