Timeline for Basic results with three or more hypotheses
Current License: CC BY-SA 2.5
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 15, 2013 at 19:04 | comment | added | The User | I do not think they count. The Baire theorem says “in a complete metric space (setting) every set with non-empty interior (one) is non-meagre (fat)”. The Banach theorem says “in the category of Banach spaces (setting) the epimorphisms (one) are precisely the open morphisms”. | |
| Mar 25, 2011 at 18:23 | comment | added | Noah Stein | I just wanted to point out that the Banach (or Open Mapping) theorem should have a surjectivity hypothesis. Preferring to remain agnostic about what constitutes a single hypothesis for the sake of this thread, I don't want to add it myself, but I thought I should at least mention it lest someone be mislead about the technical content. | |
| Oct 22, 2010 at 15:41 | comment | added | gowers | Just to be clear, the Arzela-Ascoli theorem is meant as an example with TWO hypotheses. I count everything in the first sentence as background. So it was not supposed to be an example of what I was looking for. | |
| Oct 22, 2010 at 15:40 | comment | added | Denis Serre | @Andreas. Thanks for the correction. | |
| Oct 22, 2010 at 15:27 | comment | added | Denis Serre | Tim, I must be dumb, but I don't see any difference between the structures of your example (Ascli-Arzela) and Krein-Milman. I give up. | |
| Oct 22, 2010 at 15:10 | comment | added | gowers | These ones don't quite count, because the hypotheses are referring to different things (e.g. see my additional remark above). For instance, I regard your first hypothesis of the Krein-Milman theorem as setting the scene, and there are only two hypotheses concerning the subset. | |
| Oct 22, 2010 at 13:46 | history | edited | Andreas Blass | CC BY-SA 2.5 |
added "open" to hypothesis of Baire's theorem; without "open" it's false.
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| Oct 22, 2010 at 11:54 | history | answered | Denis Serre | CC BY-SA 2.5 |