# Compact and perfect sets

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

Â© BrainMass Inc. brainmass.com February 24, 2021, 2:32 pm ad1c9bdddfhttps://brainmass.com/math/geometry-and-topology/compact-and-perfect-sets-27184

#### Solution Preview

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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#### 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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