OK, for metric spaces there are apparantly 3 different possibilities for the distance function in M where M is the usual Euclidean Plane:(adsbygoogle = window.adsbygoogle || []).push({});

(A) D(u,v) = sqrt((x_{1}-x_{2})^{2 }+ (y_{1}-y_{2})^{2})

(B) D(u,v) = max(|x_{1}-x_{2}|,|y_{1}-y_{2}|)

(C) D(u,v) = |x_{1}-x_{2}| + |y_{1}-y_{2}|

which somehow correspond to the picture I have attached.

A corresponds to the circle, B to the square and C to the diamond(this is supposed to be a square diamond but i created the image in paint, sorry)

Now, I understand (A) but I cannot seem to understand why (B) and (C) end up looking this way. and to be honest, I dont understand B and C at all.

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# Metric Spaces-BASIC DISTANCE

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