I am taking an undergraduate algebraic geometry course this semester, and I will probably be on here a lot! Anyways, my first question is if this is the correct forum to be posting my future questions on? If not, if someone could move my post, I would greatly appreciate it!

I have a couple small examples that I need to show for next class but I am a little rusty on some definitions and how to interpret them into my solutions.

(1) Find a continuous bijection which is not a homomorphism.

(2) Show that the open ball $\displaystyle B^n = ${$\displaystyle (x_1,....,x_n) \in \mathbb{R}^n | x^{2}_1 + ... + x^{2}_n < 1$} in $\displaystyle \mathbb{R}^n$ is homomorphic to $\displaystyle \mathbb{R}^n$

I am so lost it's not even funny, especially on the 2nd problem...

Thanks for looking.