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Math Help - convergence in the product and box topology

  1. #1
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    convergence in the product and box topology

    Hi. Can I have some help in answering the following questions? Thank you.

    Let {f_n} be a sequence of functions from N(set of natural numbers) to R(real nos.) where
    f_n (s)=1/n if 1<=s<=n
    f_n (s)=0 if s>n.
    Define f:N to R by f(s)=0 for every s>=1.
    a) Does {f_n} (n=1 to inf) converge to f in the R^N (cartesian product) endowed with the product topology?
    b) when endowed with the box topology?

    Thanks again.
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  2. #2
    Senior Member Tinyboss's Avatar
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    Consider the open set (in the box topology) given by \prod_{n=1}^\infty(-\frac1{n+1},\frac1{n+1}).
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