Prove that in the cartesian metric space $(E, \rho)$ of the metric spaces $(E_i, \rho_i), \; \; i=1, \dots, n$ hold the relations:
i. $\rho_i(x_i, y_i) \leq \rho(x, y)$
ii. $\displaystyle \rho(x, y) \leq \sum_{i=1}^{n} \rho_i (x_i, y_i) $
Solution:
i. $\rho_i(x_i, y_i) \leq \rho(x, y)$
ii. $\displaystyle \rho(x, y) \leq \sum_{i=1}^{n} \rho_i (x_i, y_i) $
Solution:
