# Sets

See attachment

1) Let > 0 and >0, and . Show that and are - neighborhoods of for appropriate values of .

2)Let and be nonempty sets and let : have bounded range in . Let :

and be defined by

,

Prove that

We sometimes express this by writing

.

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#### Solution Preview

Please see the attachment.

Problem #1

Proof:

As a math convention, is an -neighborhood of . Similarly, is a -neighborhood of .

If , ...

#### Solution Summary

This is a proof regarding nonempty sets. The nonempty set bounded range is examined.

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