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Problem 5. Let (X, d) be a metric space, and E C X. Show that E =N{B|ECB and B is closed}. Remark: You can show this in essentially two different ways: using sequences, or the original definitions with open sets. It is a good exercise for yourself to try both!

Problem 5. Let (X, d) be a metric space, and E C X. Show that E =N{B|ECB and B is closed}. Remark: You can show this in essentially two different ways: using sequences, or the original definitions with open sets. It is a good exercise for yourself to try both!

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Metric spaces

Problem 5. Let (X, d) be a metric space, and E C X. Show that E N{B|EC B and B is closed}. Remark: You can show this in essentially two different ways: using sequences, or the original definitions with open sets. It is a good exercise for yourself to try both!
Transcribed Image Text:Problem 5. Let (X, d) be a metric space, and E C X. Show that E N{B|EC B and B is closed}. Remark: You can show this in essentially two different ways: using sequences, or the original definitions with open sets. It is a good exercise for yourself to try both!
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