3. Show that X = [0, 1] with the discrete metric is bounded but not totally bounded. %3D
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Q: 3. Show that X = [0; 1] with the discrete metric is bounded but not totally bounded
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A: the usual metric d(x,y)=|x-y| usually induces the norm.
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Q: Show that X = [0, 1] with the discrete metric is bounded but not totally bounded.
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Q: 3. Show that X = [0, 1] with the discrete metric is bounded but not totally bounded.
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![3. Show that X = [0, 1] with the discrete metric is bounded but not totally bounded.
%3D](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0855a8b1-e4e5-451f-970a-7d73f3c47f68%2F26d9a060-eb17-4b04-9459-5de4e61f42c5%2Flsilgvv_processed.jpeg&w=3840&q=75)
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- Prove that the d1 (“Manhattan”) metric on R2 is really a metric.A. Let H be the set of all points (x, y) in ℝ2 such that x2 + 3y2 = 12. Show that H is a closed subset of ℝ2 (considered with the Euclidean metric). Is H bounded?Let f:X->Y be a function between metric spaces (X,d) and (Y,d). Prove that f: (0, infinity) -> R, f(x) is not uniformly continuous.