2.I.4FMetric and Topological SpacesPart IB, 2006Which of the following subspaces of Euclidean space are connected? Justify your answers (i) {(x,y,z)∈R3:z2−x2−y2=1}\left\{(x, y, z) \in \mathbf{R}^{3}: z^{2}-x^{2}-y^{2}=1\right\}{(x,y,z)∈R3:z2−x2−y2=1}; (ii) {(x,y)∈R2:x2=y2}\left\{(x, y) \in \mathbf{R}^{2}: x^{2}=y^{2}\right\}{(x,y)∈R2:x2=y2}; (iii) {(x,y,z)∈R3:z=x2+y2}\left\{(x, y, z) \in \mathbf{R}^{3}: z=x^{2}+y^{2}\right\}{(x,y,z)∈R3:z=x2+y2}.