Interactive Real Analysis
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Real Analysis
1. Sets and Relations
2. Infinity and Induction
3. Sequences of Numbers
4. Series of Numbers
5. Topology
5.1. Open and Closed Sets
5.2. Compact and Perfect Sets
5.3. Connected and Disconnected Sets
6. Limits, Continuity, and Differentiation
7. The Integral
8. Sequences of Functions
9. Historical Tidbits
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Definition 5.2.1: Compact Sets
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A set
S
of real numbers is called compact if every sequence in
S
has a subsequence that converges to an element again contained in
S
.
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