Definition:Chebyshev Distance/Graphical Example

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Definition

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


ChebyshevDistance.png


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


Sources

Strictly speaking, the exercise specifically calls for $\map {B_\epsilon} {0; d_\infty}$ where $0 := \tuple {0, 0}$.