Which of the following spaces are connected?\\
(A) $\left\{(x,y) \in \mathbb{R}^2 \mid xy = 1\right\}$ as a subspace of $\mathbb{R}^2$;\\
(B) The set of upper triangular matrices as a subspace of $M_n(\mathbb{R})$;\\
(C) The set of invertible diagonal matrices as a subspace of $M_n(\mathbb{R})$;\\
(D) $\left\{(x,y,z) \in \mathbb{R}^3 \mid z \geq 0, z^2 \geq x^2 + y^2\right\}$ as a subspace of $\mathbb{R}^3$.