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Compact and perfect sets

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If P is a perfect set and K is compact is the intersection P intersection K always compact?always perfect?.

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Solution Summary

If P is a perfect set and K is compact is the intersection P intersection K always compact?always perfect?.

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Proof:

P is perfect if and only P=P', where P' is the set of limit points of P. K is compact. Let Q=P intersects K

1. Q is also compact.
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