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10. Let X be the set of real numbers, and let d be the pseudometric given by d(x, y) = 1 if ry, and d(x,x) = 0 (Example 1.1(e)). (a) Describe the closure of the cell C(0; 1). (b) Describe the set B(0; 1) = {y E X: d(0, y) ≤ 1}.

10. Let X be the set of real numbers, and let d be the pseudometric given by d(x, y) = 1 if ry, and d(x,x) = 0 (Example 1.1(e)). (a) Describe the closure of the cell C(0; 1). (b) Describe the set B(0; 1) = {y E X: d(0, y) ≤ 1}.

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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Topology: In your answers, include graphs of the sets you are asked to describe.
10. Let X be the set of real numbers, and let d be the pseudometric given by d(x, y) = 1 ifr #y, and d(x,x) = 0 (Example 1.1(e)). (a) Describe the closure of the cell C(0; 1). (b) Describe the set B(0; 1) = {y E X: d(0, y) ≤ 1}.
Transcribed Image Text:10. Let X be the set of real numbers, and let d be the pseudometric given by d(x, y) = 1 ifr #y, and d(x,x) = 0 (Example 1.1(e)). (a) Describe the closure of the cell C(0; 1). (b) Describe the set B(0; 1) = {y E X: d(0, y) ≤ 1}.
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