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Thread: introduction to real analysis

  1. #1
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    introduction to real analysis

    I need help with this problem:

    Let X and Y be sets that are non empty and are different. Where X is compact and Y is a closed set.
    Show that there exist xo in X and yo in Y such that |xo-yo|<= |x-y| for all x in X and y in Y.

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  2. #2
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    Re: introduction to real analysis

    I apologyze for my notation.
    I will copy once again the problem, using a better notation.

    Let X and Y be non empty sets. X is a compact set and Y is a closed set. Show that ∃ α∈X and β∈Y such that |α-β|≤|x-y| ∀ x∈X and ∀ y∈Y
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  3. #3
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    Re: introduction to real analysis

    Hi,
    I hope the following solution is understandable to you. If you have questions, post them and I'll try to answer.

    Thanks from Yeison
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