Question 1.1.16 from Hatcher:
Show that there are no retractions $r : X\to A$ for the case $X = \mathbb{R}^3$, $A$ any subspace homeomorphic to $S^1$.
There's a bunch of other cases too, but I'd just like help as to how to go about this sort of question. I can clearly visualise that there is no retraction, but how do you write this?