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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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https://brainmass.com/math/algebraic-geometry/nonempty-set-bounded-range-182790

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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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