Timeline for Fixed point theorem for the uncountable power of an interval
Current License: CC BY-SA 4.0
14 events
| when toggle format | what | by | license | comment | |
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| Dec 24, 2022 at 14:37 | comment | added | Alessandro Della Corte | @AsafKaragila Sorry if that wasn't a very useful comment... but I never met $\omega$ as a viable notation for a cardinal, and the existence of the Long Line (for which the use of an ordinal is essential) genuinely confused me. I admit it'd been a pointless question for the long line, though... | |
| Dec 24, 2022 at 0:17 | comment | added | Asaf Karagila♦ | @AlessandroDellaCorte: Despite the fact that I generally try to separate cardinals and ordinals, it is fairly common to use $\omega$ as both and let the context (which was very clear here) to dictate the meaning. "Go left!" can be understood as a driving instruction or a political slogan. It's the greater context which determines which one is the meaning... | |
| Dec 23, 2022 at 22:25 | answer | added | KP Hart | timeline score: 11 | |
| Dec 23, 2022 at 15:55 | comment | added | Michael Greinecker | What @terceira wrote. By the Schauder-Tikhonov fixed point theorem: Every continuous function from a nonempty compact convex subset of a locally convex TVS to itself has a fixed point. | |
| Dec 23, 2022 at 14:39 | history | edited | Tyrone |
edited tags
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| Dec 23, 2022 at 9:13 | comment | added | terceira | Yes. This is a special case of the Schauder fixed point theorem. | |
| Dec 23, 2022 at 5:19 | answer | added | Joseph Van Name | timeline score: 7 | |
| Dec 23, 2022 at 2:53 | history | became hot network question | |||
| Dec 22, 2022 at 21:27 | history | edited | user494312 | CC BY-SA 4.0 |
added 10 characters in body
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| Dec 22, 2022 at 21:25 | comment | added | user494312 | Sorry, I meant the product topology. And yes, I should say $\kappa\geq \aleph_1$. | |
| Dec 22, 2022 at 19:55 | answer | added | James E Hanson | timeline score: 9 | |
| Dec 22, 2022 at 19:25 | history | edited | Daniele Tampieri | CC BY-SA 4.0 |
Minor grammar improvements and typo fixes
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| Dec 22, 2022 at 19:19 | comment | added | Alessandro Della Corte | $\kappa>\omega$ doesn't imply uncountable. Do you really mean it? And: do you equip your space with the product topology or the lexicographic order topology (obtaining the Long Line in case $\kappa=\aleph_1$)? Since you use $\omega$ instead of $\aleph_0$ I'm in doubt. | |
| Dec 22, 2022 at 18:53 | history | asked | user494312 | CC BY-SA 4.0 |