earlier are an example of balls in a normed vector space.

-norm

In a Cartesian space with the {{mvar , that is one chooses some and definesThen an open ball around the origin with radius is given by the setFor , in a 2-dimensional plane , "balls" according to the -norm (often called the taxicab or Manhattan metric) are bounded by squares with their diagonals parallel to the coordinate axes; those according to

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