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Math Help - few claims need to check if it is right

  1. #1
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    few claims need to check if it is right

    A continuous function on closed bounded X subset of R is uniformly convergent.



    i mean,

    a uniformly convergent sequence of functions must converge to a uniformly continuous function.
    Last edited by szpengchao; October 24th 2008 at 01:10 PM.
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  2. #2
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    Quote Originally Posted by szpengchao View Post
    The uniform limit of uniformly continuous function is continuous.

    A continuous function on closed bounded X subset of R is uniformly convergent.
    Please define "uniform limit".
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  3. #3
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    Quote Originally Posted by szpengchao View Post
    A continuous function on closed bounded X subset of R is uniformly convergent.
    a uniformly convergent sequence of functions must converge to a uniformly continuous function.
    If that is your meaning of "uniform limit", then the limit function is continuous.

    A continuous function on closed bounded X subset of R is uniformly continuous.
    This is also true because closed bounded X subset of R are compact.
    Last edited by Plato; October 25th 2008 at 04:33 AM.
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  4. #4
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    ok.

    Quote Originally Posted by Plato View Post
    If that is your meaning of "uniform limit", then the limit function is continuous.

    A continuous function on closed bounded X subset of R is uniformly convergent.
    This is also true because closed bounded X subset of R are compact.

    Are you sure that the second one is true?

    i mean, uniformly convergent. not uniformly continuous.
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  5. #5
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    I have corrected that typo.
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