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Math Help - Properties of Continuous Function

  1. #1
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    Exclamation Properties of Continuous Function

    I am completely lost for the following question. Can someone help?

    If is continuous and A is a bounded subset of , prove that . Is this necessarily true if A is not bounded?
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  2. #2
    Senior Member Tinyboss's Avatar
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    What if A is all of \mathbb{R}^p? What's \overline{A}? What if F(A) is open and not all of \mathbb{R}^p?
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