1. Let $\displaystyle A=\{x\in R^3:x_2\geq 2, x_1^2+x_3^2=1\}$

Find $\displaystyle A^\circ,\overline{A}$ and explain.

id say that interior is empty set and closure is A, but if so, how to show that?

2. Let $\displaystyle A=\{\|x\|_{max}\leq 2,x\in\mathbb{R}^2\}$ and $\displaystyle B=\{x^2-y^2>1,(x,y)\in\mathbb{R}^2\}$. Let $\displaystyle C=A\cap B$. i dont know how exactly its called but: is C partly opened with respect to A, or partly closed?

definition: Y is partly opened with respect to X if and only if there exists opened set $\displaystyle G\in\mathbb{R}^d$ such that $\displaystyle Y=G\cap X$