Example 1.5. Let X = R? x R² and d : X R, such that,(1) d (x, y) = d1(x1, 82), (Yı, 42)) =| x1 – Yı |+ | x2 – 2 |(2) d2(x, y) = d2((x1, r2), (y1, Y2)) = Max{| x1 – yı |,| x2 – y2 |}%3DThen (X, d1) and (X, d2) are metric spaces.Proof. Exercise.

Answered: Image /qna-images/answer/8d16c853-aff6-4d41-9cc0-63dfc170fea3.jpg

Example 1.5. Let X = R? x R² and d1 : X R, such that, (1) di(x, y) = d;((r1, 12), (Y1, Y2)) =| ¤1 – Yı |+ | #2 – 42 | (2) d2(x, y) = d2((x1, T2), (Y1; 42)) = Max{| x1 – Y1 |;| #2 – 2 |} Then (X, d1) and (X, d2) are metric spaces. Proof. Exercise.

Example 1.5. Let X = R? x R² and d1 : X R, such that, (1) di(x, y) = d;((r1, 12), (Y1, Y2)) =| ¤1 – Yı |+ | #2 – 42 | (2) d2(x, y) = d2((x1, T2), (Y1; 42)) = Max{| x1 – Y1 |;| #2 – 2 |} Then (X, d1) and (X, d2) are metric spaces. Proof. Exercise.

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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Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.

Question

Example 1.5. Let X = R? x R² and d : X R, such that,
(1) d (x, y) = d1(x1, 82), (Yı, 42)) =| x1 – Yı |+ | x2 – 2 |
(2) d2(x, y) = d2((x1, r2), (y1, Y2)) = Max{| x1 – yı |,| x2 – y2 |}
%3D
Then (X, d1) and (X, d2) are metric spaces.
Proof. Exercise.

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