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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

    .

    © BrainMass Inc. brainmass.com October 9, 2019, 9:23 pm ad1c9bdddf
    https://brainmass.com/math/algebraic-geometry/nonempty-set-bounded-range-182790

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    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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