2. Using the sequence z n, show that (R, d) is not a compact space. 3. Deduce.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.3: Trigonometric Functions Of Real Numbers
Problem 65E
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part 2 3 topology campact
7. Deduce.
Exercise 2.
Consider the following metric defined on R by
d(x, y) = inf{|ryl, 1}.
1. Is (R, d) bounded?
2. Using the sequence = n, show that (R, d) is not a compact space.
3. Deduce.
Transcribed Image Text:7. Deduce. Exercise 2. Consider the following metric defined on R by d(x, y) = inf{|ryl, 1}. 1. Is (R, d) bounded? 2. Using the sequence = n, show that (R, d) is not a compact space. 3. Deduce.
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