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Exercise 3. In this exercise (X, d) is a metric space. .} 2) Assume there exists r> 0 and a sequence (an)neN in the metric space X with d(a,,a,) ≥r, for all i, j EN with ij. Show that X is not compact.

Exercise 3. In this exercise (X, d) is a metric space. .} 2) Assume there exists r> 0 and a sequence (an)neN in the metric space X with d(a,,a,) ≥r, for all i, j EN with ij. Show that X is not compact.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 10E
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Exercise 3. In this exercise (X, d) is a metric space. } 2) Assume there exists r> 0 and a sequence (an)neN in the metric space X with d(a,,a,) ≥r, for all i, jEN with ij. Show that X is not compact.
Transcribed Image Text:Exercise 3. In this exercise (X, d) is a metric space. } 2) Assume there exists r> 0 and a sequence (an)neN in the metric space X with d(a,,a,) ≥r, for all i, jEN with ij. Show that X is not compact.
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