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Milton
Frequent VisitorJoined: 27 Oct 2003Posts: 266
Location: HKUST Math
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Posted: Sun May 22, 2005 11:49 pm Post subject: boundedness of f’ and uniform continuity of f
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Suppose exists on and bounded. It is not difficult to see that is uniformly continuous. Is the converse true?_________________Sometimes Truth is meanlingless;What means is how you believe in.
偶爾，真相並沒有意義；意義在於你怎樣相信。
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wingdeathscythe
Joined: 24 Jan 2004Posts: 13
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Posted: Tue May 24, 2005 10:01 am Post subject:
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The well known construction (by weierstrass?) of a nowhere differentiable, but continuous, function may serve as a counterexample.[/tex]
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Milton
Frequent VisitorJoined: 27 Oct 2003Posts: 266
Location: HKUST Math
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Posted: Tue May 24, 2005 11:14 am Post subject:
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Oh, let me state the question clearly. Sorry to leave such an ambiguity.
Suppose exists and is undounded. Can be uniformly continuous?
_________________Sometimes Truth is meanlingless;What means is how you believe in.
偶爾，真相並沒有意義；意義在於你怎樣相信。
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