8. Give an example to show that the arbitrary intersection of open sets is not an open set. 9. Give an example of a set which neither closed nor open. 10. Show by an example that a nonempty proper subset of 5 in the metric space (S, d) can be both open and closed.

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8. Give an example to show that the arbitrary intersection of open sets is not an open set.
9. Give an example of a set which neither closed nor open.
10. Show by an example that a nonempty proper subset of 5 in the metric space (S, d) can be
both open and closed.
Transcribed Image Text:8. Give an example to show that the arbitrary intersection of open sets is not an open set. 9. Give an example of a set which neither closed nor open. 10. Show by an example that a nonempty proper subset of 5 in the metric space (S, d) can be both open and closed.
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