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I was trying to figure out if the following is a metric space in R x R (Cartesian product).

D[(x1,y1),(x2,y2)] = min( abs(x1-x2), abs(y1-y2) )

I know there are four properties to confirm that the following is a metric space but I'm having trouble with the "triangle inequality" for the distance function.

So, I have D[(x1,z1),(x2,z2)] should be less than or equal to D[(x1,y1),(x2,y2)] + D[(y1,z1),(y2,z2)].

D[(x1,z1),(x2,z2)] = min( abs(x1-x2), abs(z1-z2) ) and basically I'm stuck on the next step. How do I configure it such that I could put it in the form of D[(x1,y1),(x2,y2)] + D[(y1,z1),(y2,z2)]?

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# Homework Help: Metric Spaces and Topology

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