Definition:Taxicab Metric/Graphical Example

Definition
This diagram shows the open $\epsilon$-ball $\map {B_\epsilon} {A; d_1}$ of point $A$ in the $\struct {\R^2, d_1}$ metric space where $d_1$ is the taxicab metric.


 * TaxicabMetric.png

Note that $\epsilon = \epsilon_1 + \epsilon_2$.

Neither the boundary lines nor the extreme points are actually part of the open $\epsilon$-ball.