- Analysis Functional 1 (26.15 KiB) Viewed 34 times
Analysis Functional
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answerhappygod
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Analysis Functional
Analysis Functional
Exercise 2. 1. Consider the map d: Rx RR given by d(x, y) = 3x² - 4y²1. Does (R, d) is a metric space? 2. Consider the map d: Rx R→ R given by x-2y if x ≥ 2y d(x, y) = { √2 if x <y. Does (R, d) is a metric space? 3. Let n E N. Consider the map d: R" x RR given by 72 d(x, y) = x-yj|t. (i) Prove that (R", d) is a metric space. (ii) Prove that the map xd(x, 0) is not a norm on R".
Exercise 2. 1. Consider the map d: Rx RR given by d(x, y) = 3x² - 4y²1. Does (R, d) is a metric space? 2. Consider the map d: Rx R→ R given by x-2y if x ≥ 2y d(x, y) = { √2 if x <y. Does (R, d) is a metric space? 3. Let n E N. Consider the map d: R" x RR given by 72 d(x, y) = x-yj|t. (i) Prove that (R", d) is a metric space. (ii) Prove that the map xd(x, 0) is not a norm on R".