Timeline for Fixed point theorems
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Dec 19, 2022 at 13:56 | history | edited | Martin Sleziak | CC BY-SA 4.0 |
http -> https (the question was bumped anyway)
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| May 28, 2013 at 6:55 | comment | added | Zach N | Application: The (Cantor–)Schroeder-Bernstein Theorem. The proof is described in the second paragraph of this answer: mathoverflow.net/questions/42485/…. | |
| Apr 11, 2013 at 20:43 | comment | added | Martin Brandenburg | Sure. I wish I could edit comments. In the link the statement is correct ;). | |
| Apr 10, 2013 at 20:14 | comment | added | Todd Trimble | @Martin: no, you also need for $F$ to preserve colimits of $\omega$-chains. (E.g., otherwise you could prove that the covariant power-set functor on $Set$ has an initial algebra, which would run counter to Cantor's theorem.) | |
| Apr 10, 2013 at 13:10 | comment | added | Martin Brandenburg | More generally, if $C$ is a category with colimits of $\omega$-chains and an initial object $0$, then every functor $F : C \to C$ has an initial $F$-algebra (namely the colimit of $0 \to F(0) \to F(F(0)) \to \dotsc$). Actually this gives a neat construction of the Banach space $L^1([0,1])$, including the integral $L^1([0,1]) \to \mathbb{R}$, see mathoverflow.net/questions/23143 | |
| Apr 10, 2013 at 6:04 | history | answered | Nate Ackerman | CC BY-SA 3.0 |