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Vijay posted an Question
August 27, 2022 • 16:50 pm 30 points
  • CSIR NET
  • Mathematical Sciences

Ove two metie spaces 1, di) and (x2, d,), the cartesian product x1 x xz can be macae nto a metric space in many ways. we can define d: (x, x x,) x (x, x x) r by

Ove two metie spaces 1, di) and (X2, d,), the cartesian product X1 x Xz can be macae nto a metric space in many ways. We can define d: (X, x X,) x (X, x X) R by any one oI the following formulae 121 1/2 (ii) d((, 32), O1. y2)) = max. {d,(1. y), da(X2. y2)}. Prove that each formula defines a metric on X x X2. (The first metric is called the Pythagorean metric).

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