Question

(a) On R2, prove that di ((zı, y), (z2W2)) := Izı-zal + ly,-Val is a metric. (b) Assume that doc ( (zi, yī), (z2,p)) := maxlz-zal, lyi-yl} is a metric on R2 for each p 21. Prove that di and d induce the same topology on R2. You may use the following lemma (but do not need to prove it): Lemma: Let d and d' be two metrics on aset X; let T and T' be the topologies the induce respectively. Then T, is finer than T if and only if for each z E X and each ε > 0, there exists a δ > 0 such that

Answer 1

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