Notation Question: What does $B(0,1)$ mean when it comes to metric spaces?

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I have to draw the unit balls $B(0,1)$ in $\mathbb{R}^2$ with respect to several metrics, however I am not certain whether this means a unit ball centered at $(0,1)$ or at $(0,0)$? Thanks for your help, hopefully it is an easy question just the book I have uses different notation.

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2 Answers

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B(0,1) means the unit ball with center in (0,0) and with radius 1. But the unit ball need not always be a circle! In Euclid (usual) metric space it is a circle, but there are other metrics in which it takes other forms (see unit balls for metric spaces generated by 1 and maximum norms).

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$B(0,1)$ usually means a unit ball centered at the point $\vec 0 = (0,0)$.

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