# Compactness Proof

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Assume that and are two equivalent norms on X, and that . Prove that M is compact in if and only if M is compact in .

https://brainmass.com/math/discrete-math/compactness-two-equivalent-norms-67855

#### Solution Preview

Please see the attachment.

Assume that and are two equivalent norms on X, and that . Prove that M is compact in if and only if M is compact in .

Proof:

Since and are equivalent, then ...

#### Solution Summary

This is a proof regarding compactness.

$2.19