I am trying to show that an "epsilon ball in the taxicab metric" can be contained in a "epsilon ball in the usual metric".(adsbygoogle = window.adsbygoogle || []).push({});

Let "Up" be a taxicab ball, and "Ud" be a usual metric ball.

How can I show that Up( (x,y) , e ) is a subset of Ud( (x,y), e ) ?

I have drawn the picture and I understand how the taxicab ball is inside. It is a diamond that touches the usual ball on each of the diamond's four corners and is less than everywhere else.

How can I show this algebraically?

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# Homework Help: Usual and taxicab metric topologies

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