Metric spaces examples Problem 1. Give examples of a metric space (X, d) and:(a) an open set that is not closed,(b) a closed set that is not open,(c) a set (different from 0, X) that is both open and closed.(d) a set that is not open, nor closed.(In particular: Not open # closed!!!)

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Answered: Problem 1. Give examples of a metric…

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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Problem 1. Give examples of a metric space (X, d) and: (a) an open set that is not closed, (b) a closed set that is not open, (c) a set (different from Ø, X) that is both open and closed. (d) a set that is not open, nor closed. (In particular: Not open # closed!!!)