Timeline for Ultraproducts of Banach spaces versus model theoretic ultraproduct
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
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| May 4, 2023 at 15:16 | vote | accept | Anthony D'Arienzo | ||
| May 3, 2023 at 13:05 | comment | added | Jochen Wengenroth | Categorical products may look very diffently in different categories, isn't it thus quite clear that the same holds for ultraproducts? | |
| May 3, 2023 at 6:17 | comment | added | YCor | Indeed, in case you're using both constructions, you might need to modify the terminology, e.g., calling the second construction "reduced ultraproduct" or "metric ultraproduct" (which makes sense without changes in pointed metric spaces in general, without change). | |
| May 3, 2023 at 6:14 | history | edited | YCor | CC BY-SA 4.0 |
formatting, added tags
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| May 3, 2023 at 1:19 | history | became hot network question | |||
| May 3, 2023 at 0:39 | comment | added | Yemon Choi | "it seems confusing to call both constructions an ultraproduct" - there is always a trade-off in mathematical terminology between precision and practical necessity. In the world of Banach spaces, Banach algebras and operator algebras, the "ultraproduct" construction is extremely useful and it would become unwieldy to constantly append an adjective clarifying that this is not the model-theoretic ultraproduct. | |
| May 2, 2023 at 19:29 | comment | added | Jochen Glueck | Maybe that's a bit naive, but isn't the reason simply that both constructions have the same goal? You want to ignore what happens outside the filter but want to stay in the "right" category. | |
| May 2, 2023 at 19:14 | answer | added | Andreas Blass | timeline score: 16 | |
| May 2, 2023 at 18:57 | answer | added | Alex Kruckman | timeline score: 18 | |
| May 2, 2023 at 18:52 | answer | added | Terry Tao | timeline score: 11 | |
| May 2, 2023 at 17:20 | history | edited | Anthony D'Arienzo | CC BY-SA 4.0 |
Typo
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| May 2, 2023 at 17:15 | history | asked | Anthony D'Arienzo | CC BY-SA 4.0 |