Interactive Real Analysis - part of MathCS.org

• 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
• Java Tools

Example 5.2.10(b):

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Is the set {1, 1/2, 1/3, ...} perfect ? How about the set {1, 1/2, 1/3, ...} {0} ?

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• The first set is not closed. Hence it is not perfect.
• The second set is closed, and {0} is an accumulation point. However, every point different from 0 is isolated, and can therefore not be an accumulation point. Therefore, this set is not perfect either.