Timeline for About the axiom of choice, the fundamental theorem of algebra, and real numbers
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 7, 2022 at 21:28 | comment | added | François G. Dorais | @LSpice The quotient of $\mathbb{C}^n$ under permutation of coordinates. | |
| Nov 7, 2022 at 18:31 | comment | added | LSpice | @FrançoisG.Dorais, what is the topology on multisets according to which that function is continuous? | |
| Jun 21, 2012 at 22:29 | comment | added | François G. Dorais | I was looking for a reference for this result of Ernst Specker, here it is: MR0256880 ams.org/mathscinet-getitem?mr=256880 Note that the result is peculiar: For each $m \geq 1$ there is a continuous function that returns the $m$-element multiset of the roots of the (not necessarily irreducible) polynomial of degree $m$, but there is no continuous function that picks just one element from that multiset except in the case $m = 1$! | |
| Jun 21, 2012 at 22:27 | history | edited | Goldstern | CC BY-SA 3.0 |
example of a choice without AC
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| Jun 21, 2012 at 21:15 | history | answered | Goldstern | CC BY-SA 3.0 |