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Math Help - Supremum of Continuous functions

  1. #1
    Newbie
    Joined
    Jan 2011
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    Supremum of Continuous functions

    Hi,

    I need an example to show that the supremum of continuous functions is a lower semi continuous function (not a continuous function).

    Thanks
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  2. #2
    Junior Member
    Joined
    Jun 2010
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    54
    Let f_{n}(x)=|x|^{1/n}\ \ n\geq 1

    Can you find the piecewise definition of sup\ f_{n}(x)?
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