Closed set
is closed when every sequence in that converges in has its limit in : closedness is sealed against taking sequential limits.
Examples
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is closed and so is .
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, , and are not closed: for instance lies in each of them and converges to , which is outside all three.
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is not closed.
Related
Stated in
- Definition 2.16 (Closed Set)§2.3 Extreme Value Theorem