## The New York metric with an open ball

The New York metric $$\rho_N$$ (known also as the $$L_1$$ norm) on $$\mathbb R^2$$ is defined as $\rho((x_1, x_2),(y_1, y_2)) = |x_1 - y_1| + |x_2 - y_2|,$ kde $$(x_1, x_2), (y_1, y_2) \in \mathbb R^2$$.
Show that $$(\mathbb R^2, \rho_N)$$ is a metric space.
Draw the open ball with center $$(1, 1)$$ and radius $$2$$ v $$(\mathbb R^2, \rho_N)$$.