3. Consider the metric space (R..|) and let S be the union given by(0}U UIJ. Note that each of the [n) is a real interval.a) Is S open in R? Explain why or why not.b) What is the set of all limit points of S?c) Does the boundary aS exist? If so, what is it equal to? If not, explainwhy.

Answered: Image /qna-images/answer/df6f605b-93a2-4796-8aa9-8c3229d332d1.jpg

Answered: 3. Consider the metric space (R..|) and…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

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3. Consider the metric space (R..|) and let S be the union given by (0}U UI J. Note that each of the [ n) is a real interval. a) Is S open in R? Explain why or why not. b) What is the set of all limit points of S? c) Does the boundary aS exist? If so, what is it equal to? If not, explain why.