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Injection from R2 to R

Posted: Sun Mar 06, 2011 4:24 pm
by nayel
Find an injection from $\mathbb R^2\to\mathbb R$.

Re: Injection from R2 to R

Posted: Mon Mar 07, 2011 2:51 am
by tanvirab
Interesting. A classic space-filling curve should work. Are there easier solutions?

Re: Injection from R2 to R

Posted: Mon Mar 07, 2011 4:16 pm
by nayel
Should be, as it was on one of our examples sheets. And I don't even know what that term means :P

Re: Injection from R2 to R

Posted: Wed Mar 23, 2011 12:27 am
by Avik Roy
There's one that maps all the points in $(0,1) \times (0,1)$ to $(0,1)$. Take $(0.a_1a_2a_3 ... ,0.b_1b_2b_3 ...) \rightarrow 0.a_1b_1a_2b_2a_3b_3...$. Such a map should work also

Re: Injection from R2 to R

Posted: Thu Mar 24, 2011 5:56 pm
by nayel
Yep that should work.