Timeline for functions satisfying "one-one iff onto"
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Aug 27, 2019 at 16:30 | comment | added | LSpice | @TomLeinster, of course it's very silly, but, if you want your $f$ to be surjective, then $S$ had better be $[0, 1)$, not $[0, 1]$. | |
| Mar 31, 2012 at 14:04 | comment | added | gowers | Does $f$ have to be continuous, or something like that? Otherwise, the result seems to be trivially false because you can mess about with the map on a set of measure zero. | |
| Feb 20, 2012 at 11:40 | comment | added | Tom Leinster | Actually, I don't get it. Take n = 1 and S = [0, 1]. Take the map f: S --> S defined by f(x) = 2x (mod 1). Then f is measure-preserving (wrt the usual measure) and surjective, but not injective. Maybe you mean something different by "volume-preserving"...? I had a look in Agarwal and Pach's book, but couldn't find a clean statement of the result to which you're alluding. | |
| Feb 18, 2012 at 9:03 | history | edited | Erik Aas | CC BY-SA 3.0 |
fixed grammar
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| Feb 17, 2012 at 21:51 | history | made wiki | Post Made Community Wiki by François G. Dorais | ||
| Feb 17, 2012 at 21:07 | history | answered | Erik Aas | CC BY-SA 3.0 |