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Let X be a non-empty set and d be a metric on X. (a) Write down the following. ii. An open ball of radius r and centered at x EX in terms of d, and use this notion of open ball to explain the concept of open subset O of X. (b) Suppose X = R², x = (1, 1) E R2 and r = 3. Sketch the d-closed ball of radius r and centered at x if i. d is the Euclidean metric on R2. ii. d is the max metric on R2. iii. d is the taxi-cap metric on R².

Let X be a non-empty set and d be a metric on X. (a) Write down the following. ii. An open ball of radius r and centered at x EX in terms of d, and use this notion of open ball to explain the concept of open subset O of X. (b) Suppose X = R², x = (1, 1) E R2 and r = 3. Sketch the d-closed ball of radius r and centered at x if i. d is the Euclidean metric on R2. ii. d is the max metric on R2. iii. d is the taxi-cap metric on R².

Advanced Engineering Mathematics
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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Let X be a non-empty set and d be a metric on X. (a) Write down the following. ii. An open ball of radius r and centered at x EX in terms of d, and use this notion of open ball to explain the concept of open subset O of X. (b) Suppose X = R², x = (1, 1) E R2 and r = 3. Sketch the d-closed ball of radius r and centered at x if i. d is the Euclidean metric on R2. ii. d is the max metric on R2. iii. d is the taxi-cap metric on R². Page 2 o
Transcribed Image Text:Let X be a non-empty set and d be a metric on X. (a) Write down the following. ii. An open ball of radius r and centered at x EX in terms of d, and use this notion of open ball to explain the concept of open subset O of X. (b) Suppose X = R², x = (1, 1) E R2 and r = 3. Sketch the d-closed ball of radius r and centered at x if i. d is the Euclidean metric on R2. ii. d is the max metric on R2. iii. d is the taxi-cap metric on R². Page 2 o
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