Advanced Calculus: Difference between revisions

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Intersection of infinitely many open sets can be closed.
Intersection of infinitely many open sets can be closed.
===Compact===
===Compact===
Compactness is a generalization of closed and bounded.<br>
;Definitions
* (Sequence) A set is sequentially compact if for every sequence from the set, there exists a subsequence which converges to a point in the set.
* (Topology) A set is compact if for every covering by infinitely many open sets, there exists a covering by a finite subset of the open sets.
;Notes
* A set is sequentially compact iff it is closed and bounded
===Metric Space===
===Metric Space===