1. Consider the identity function 1R2: R2 + R2, and the Euclidean and railway metrics d2 and D on R2. (a) Prove that 1R2

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1 Consider The Identity Function 1r2 R2 R2 And The Euclidean And Railway Metrics D2 And D On R2 A Prove That 1r2 1 (93.05 KiB) Viewed 46 times

1. Consider the identity function 1R2: R2 + R2, and the Euclidean and railway metrics d2 and D on R2. (a) Prove that 1R2 is (D, d2)-continuous, i.e. it is a continuous function from (R2,D) to (R2,d2). [Marks: 2] (b) Prove that 1 R2 is not (d2,D)-continuous. (Hint: Recall that we have seen a sequence in R2 which converges with respect to d2, but not with respect to D.) [Marks: 3]