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Take the set of points 1/n for all integers n. This is an isolated set of points- that is, for any of them there is an open ball about the point not containing any other point. However, this set has a limit point which is not contained in the set (namely 0), hence it is not closed.
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Earn +20 ptsQ: Is a set of isolated points a closed set?
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Continue Learning about Other Math
Are the natural numbers a Borel set?
A singleton point is a closed set. The natural numbers can be written as a countable union of points. Thus, they form a Borel set.
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