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So the set {0} is not open in the Euclidean line, is it closed? Please explain why? Is this the same for any single elem...

So the set {0} is not open in the Euclidean line, is it closed? Please explain why? Is this the same for any single element sets in the Euclidean line with the Euclidean metric? How does this change in other metric spaces? Please give some examples.
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