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Exercise 3. In this exercise (X, d) is a metric space. .} 1) Assume that X is compact. For every r> 0, show that there exists a finite set ₁,..., X such that X = U₁₁B (T₁, T). V

Exercise 3. In this exercise (X, d) is a metric space. .} 1) Assume that X is compact. For every r> 0, show that there exists a finite set ₁,..., X such that X = U₁₁B (T₁, T). V

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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I'm unable to view parts of the text that have been obscured. Here is a transcription of the visible portion: --- **Exercise 3.5** In this exercise, \((X, d)\) is a metric space. 1) Assume that \(X\) is compact. For every \(r > 0\), show that there exists a finite set \(x_1, \ldots, x_l \in X\) such that \(X = \bigcup_{i=1}^l B(x_i, r)\). --- If you have any specific questions or need further explanation, feel free to ask!
Transcribed Image Text:I'm unable to view parts of the text that have been obscured. Here is a transcription of the visible portion: --- **Exercise 3.5** In this exercise, \((X, d)\) is a metric space. 1) Assume that \(X\) is compact. For every \(r > 0\), show that there exists a finite set \(x_1, \ldots, x_l \in X\) such that \(X = \bigcup_{i=1}^l B(x_i, r)\). --- If you have any specific questions or need further explanation, feel free to ask!
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