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Thread: Can someone give an example on uniformly bounded sequence but not equicontinuous at 0

  1. April 20th 2010, 08:33 AM #1
    copyfriend
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    Can someone give an example on uniformly bounded sequence but not equicontinuous at 0

    Can someone give an example on uniformly bounded sequence of continuous functions on B(0,1) but not equicontinuous at 0?

    Thanks everyone.
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  2. April 20th 2010, 12:40 PM #2
    Opalg
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    Quote Originally Posted by copyfriend View Post
    Can someone give an example on uniformly bounded sequence of continuous functions on B(0,1) but not equicontinuous at 0?
    How about f_n(x) = \sin nx?
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