/sci/ - Science & Math

>>11464170
IIRC, that didn't work as stated.
Set [math]E = \mathbb{R}^2[/math], [math]Y= \mathbb{R}[/math].
Take polar coordinates, and then [math]f(r, \theta ) = r\frac{1}{2 \pi - \theta}[/math]. Since [math]\theta \in [0, \2pi)[/math] it's actually well defined, and for any [math]x \in \mathbb{R}^2[/math], we naturally have that [math] \lim _{r \rightarrow 0} r \frac{1}{2 \pi - \theta} = 0[/math] for fixed [math]\theta[/math], but it's fairly intuitive why there are sequences which converge to zero whose images explode (finding one explicitly is left as an exercise to the reader).
Note: this kind of proof is exactly the kind I'd completely fuck up. Reread everything five times.
Is [math]f[/math], dare I guess, continuous?