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Let X be the set of real numbers, and let d be the pseudometric given by d(z. y) = 1 if z #y, and d(z, z) = 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}.

Let X be the set of real numbers, and let d be the pseudometric given by d(z. y) = 1 if z #y, and d(z, z) = 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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Pseudometric spaces
30 Chapter 1 Pseudometric Spaces Exercises 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}.
Transcribed Image Text:30 Chapter 1 Pseudometric Spaces Exercises 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}.
Expert Solution
Introduction

As per the question we are given the set X of real numbers and the pseudometric d defined on X by d(x,y) = 1, if x ≠ y and d(x,x) = 0 otherwise.

Now we have to describe :

  1. the closure of the cell C(0;1)
  2. the set B(0;1) = {y ∈ X : d(0, y) ≤ 1}
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