Let X = R? , and let d2 be the usual, Euclideanmetric on X . Define another metric,d : X x X → R , by lettingd(x, y) := max{|1 – Yı|, |æ2 – Y2|}for any x, y E X. Which of the followingstatements is true?If a subset U CX is closed for the metric d , thenit is also closed for the metric d2 .d(x, y) < d2 (x, y) for all x, y EX, and hence ifUCX is closed for d and VC X is closed for d2, then UC V.d(a, y) < d2 (x, y) for all x, yEX, and hence ifUC X is closed for d and VCX is closed for d2then V CU.d2 (x, y) < d(x, y) for all x, y E X, and hence ifUC X is closed for d and V C X is closed for d2then U C V.

Name: Let X = R? , and let d2 be the usual, Euclideanmetric on X . Define a
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Description: Let X = R? , and let d2 be the usual, Euclideanmetric on X . Define another metric,d : X x X → R , by lettingd(x, y) := max{|1 – Yı|, |æ2 – Y2|}for any x, y E X. Which of the followingstatements is true?If a subset U CX is closed for the metric d ,

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Let X = R? , and let d2 be the usual, Euclidean metric on X. Define another metric, d : X x X → R, by letting d(x, y) := max{|a1 – y1|, |#2 – Y2|} for any a, y E X. Which of the following statements is true? If a subset U CX is closed for the metric d, then it is also closed for the metric d2 d(x, y) < d2 (a , y) for all a, yEX, and hence if UC X is closed for d and VC X is closed for d2 then UC V. d(x, y) < d2 (x, y) for all x, yEX, and hence if UC X is closed for d and VC X is closed for d2 then V CU. d2 (x, y) < d(x, y) for all a, y E X, and hence if UC X is closed for d and VC X is closed for d2 then U C V.

Let X = R? , and let d2 be the usual, Euclidean metric on X. Define another metric, d : X x X → R, by letting d(x, y) := max{|a1 – y1|, |#2 – Y2|} for any a, y E X. Which of the following statements is true? If a subset U CX is closed for the metric d, then it is also closed for the metric d2 d(x, y) < d2 (a , y) for all a, yEX, and hence if UC X is closed for d and VC X is closed for d2 then UC V. d(x, y) < d2 (x, y) for all x, yEX, and hence if UC X is closed for d and VC X is closed for d2 then V CU. d2 (x, y) < d(x, y) for all a, y E X, and hence if UC X is closed for d and VC X is closed for d2 then U C V.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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