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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Examples 5.2.5(a):
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Let S = [0, 1], and C = { (1/2, 1/2), (1/3, 2/3), (1/2, 3/2)}. Is C an open cover for S ?
Back
C
consists of open sets only.
The union of all sets in
C
contains
S
Therefore,
C
is an open cover for
S
.
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