I have got this problem in my exam: Check for compactness and connectedness of subspace P = $\{(x, y, z)\in \mathbb{R}^3 : z = x^2+y^2+1\}$
I think given subspace P is closed and bounded subset of $\mathbb{R}^3$ so it shoould be compact. But I am not sure with this.
How to check for connectedness?
I am stucked on this problem. I need help to understand how to solve such kind of problems?
Edit: I am not that much good in topology. I have started studying this subject. I need answer with little more explanation. Please take this pain.
Thanks for helping me